[cig-commits] r12717 - mc/2D/ConMan/trunk/doc
sue at geodynamics.org
sue at geodynamics.org
Tue Aug 26 16:47:14 PDT 2008
Author: sue
Date: 2008-08-26 16:47:13 -0700 (Tue, 26 Aug 2008)
New Revision: 12717
Modified:
mc/2D/ConMan/trunk/doc/conman.lyx
Log:
fixed typos, added todos. sent questions to wei to fwd to scott king
Modified: mc/2D/ConMan/trunk/doc/conman.lyx
===================================================================
--- mc/2D/ConMan/trunk/doc/conman.lyx 2008-08-26 18:33:43 UTC (rev 12716)
+++ mc/2D/ConMan/trunk/doc/conman.lyx 2008-08-26 23:47:13 UTC (rev 12717)
@@ -9,20 +9,53 @@
+
+
+
+\usepackage{float}
+
+\usepackage{textcomp}
+
+\usepackage{url}
+
+
+
+\makeatletter
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
+%% Bold symbol macro for standard LaTeX users
+
+
+%% Because html converters don't know tabularnewline
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
+%% LyX 1.5.4 created this file. For more info, see http://www.lyx.org/.
+%% Do not edit unless you really know what you are doing.
+
+
+
\usepackage{geometry}
+
\geometry{verbose,letterpaper,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\usepackage{float}
+
\usepackage{textcomp}
+
\usepackage{url}
+
\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
@@ -37,11 +70,15 @@
\usepackage{hyperref}
+
\let\myUrl\url
\renewcommand{\url}[1]{(\myUrl{#1})}
\makeatother
+
+
+\makeatother
\end_preamble
\language english
\inputencoding latin9
@@ -199,9 +236,12 @@
ConMan is a public domain program and is distributed free of charge to
anyone who wishes to use it and may be freely copied and modified.
ConMan is written in Standard Fortran 77 with cray pointers and runs on
- most unix systems with many fortran comilers (see Section 3.4 [TODO -- 3.4
- is placeholder section.
- Is this correct? Need label to put cross ref here]).
+ most Unix systems with many Fortran compilers (see Section 3.4
+\series bold
+[TODO -- 3.4 is placeholder section.
+ Is this correct? Need label to put cross ref here]
+\series default
+).
Porting it to other systems should be straightforward.
As with anything free it comes with no guarantees, but it has been benchmarked
against other existing codes (see Chapter
@@ -284,10 +324,14 @@
\begin_layout Itemize
King, S.D., A.
Raefsky, and B.H.
- Hager, ConMan: Vectorizing a finite element code for incompressible two-dimensi
-onal convection in the Earth's mantle,Phys.
+ Hager (1990), ConMan: Vectorizing a finite element code for incompressible
+ two-dimensional convection in the Earth's mantle,
+\emph on
+Phys.
Earth Planet.
- Int., 59, 195-208, 1990.
+ Int., 59,
+\emph default
+195-208.
\end_layout
@@ -298,8 +342,8 @@
The ConMan team requests that in your oral presentations and in your papers
that you indicate your use of this code and acknowledge the author of the
code and CIG
-\begin_inset LatexCommand url
-target "www.geodynamics.org"
+\begin_inset LatexCommand htmlurl
+target "geodynamics.org"
\end_inset
@@ -332,18 +376,20 @@
\end_layout
\begin_layout Standard
-I am going to follow a similar form to Hughes (The Finite Element Method)
- Chapter\InsetSpace ~
-1 sections 1-4.
- There are two forms we can write the equation, the strong and the weak
- form.
- You are used to seeing the strong form, but not used to seeing the weak
- form.
- The finite element method, is cast in the weak form.
+This section closely follows Hughes (
+\emph on
+The Finite Element Method
+\emph default
+) Chapter\InsetSpace ~
+1, sections 1-4.
+ There are two ways we can write the equation, the strong and the weak form.
+ More readers are probably more familiar with the strong form, and less
+ familiar with the weak form.
+ The finite element method is cast in the weak form.
In elasticity, for example, the weak form comes from a variational principal,
- such as the principal of virtual displacements.
- For viscous flow, there is also a variational form, but we will not go
- into that.
+ such as the principal of virtual displacements in elasticity.
+ For viscous flow, there is also a variational form, but we will not discuss
+ that here.
\end_layout
\begin_layout Standard
@@ -411,6 +457,7 @@
\end_layout
\begin_layout Standard
+\noindent
This choice of initial conditions allows us to examine both kinds of boundary
conditions.
The solution is trivial, but that does not matter.
@@ -466,6 +513,7 @@
\end_layout
\begin_layout Standard
+\noindent
\begin_inset Formula $\nu$
\end_inset
@@ -482,6 +530,7 @@
\end_layout
\begin_layout Standard
+\noindent
and
\begin_inset Formula $\mathcal{L}$
\end_inset
@@ -499,6 +548,7 @@
\end_layout
\begin_layout Standard
+\noindent
\begin_inset Formula $H^{1}$
\end_inset
@@ -519,6 +569,7 @@
\end_layout
\begin_layout Standard
+\noindent
where
\emph on
[K]
@@ -539,9 +590,9 @@
\begin_layout Standard
Now we have a start on the finite element method.
- I want to continue to follow Hughes; however his notation becomes quite
- difficult to keep up with.
- Now, lets begin to think about putting a solution on the computer.
+ We continue to follow Hughes; however, his notation becomes quite difficult
+ to keep up with.
+ Now, let's begin to think about putting a solution on the computer.
Because we will have a finite approximation, related to how fine we space
our grid, our solution will only approximate the real solution.
Following Hughes' notation, the solution on the grid will be denoted as
@@ -569,14 +620,14 @@
\begin_layout Standard
On a computer, we don't have a continuous solution.
- We have a solution at descrete points.
+ We have a solution at discrete points.
We need to approximate the solution between the points (in order to integrate
over the function).
We will do this with
\series bold
shape functions
\series default
- as they are usually called in the finite element language.
+, as they are usually called in the finite element language.
Hughes uses
\begin_inset Formula $N_{A}A=1,2,\cdots,n$
\end_inset
@@ -630,8 +681,8 @@
\begin_layout Standard
In the next section we will make the shape functions more concrete.
- I want you to see how general this is, because in principle there is a
- great deal of flexibility in how we choose the shape functions.
+ It is useful to see how general this is, because in principle there is
+ a great deal of flexibility in how we choose the shape functions.
\end_layout
\begin_layout Standard
@@ -758,7 +809,7 @@
\end_inset
- Everything in Equation\InsetSpace ~
+Everything in Equation\InsetSpace ~
\begin_inset LatexCommand ref
reference "eq:feform"
@@ -779,7 +830,7 @@
\end_inset
unknowns.
- We can think of the left hand side as a matrix,
+ We can think of the left-hand side as a matrix,
\begin_inset Formula $K_{AB}$
\end_inset
@@ -811,7 +862,7 @@
\end_inset
- By tradition,
+By tradition,
\begin_inset Formula $\left[K\right]$
\end_inset
@@ -834,24 +885,23 @@
\end_layout
\begin_layout Standard
-At this point, I will narrow the focus to deal with specifically the elements
- in my code, ConMan.
+At this point, we narrow the focus to deal with specifically the elements
+ in ConMan.
It is possible to think very general shape functions, but in practice,
- people use triangles or quadralaterals (in 2-D).
- We will extend our finite element formulation to a 2-D equation next time.
+ people use triangles or quadralaterals (in 2D).
In terms of the level of approximation, there are also a lot of possibilities.
- We will stick to the simplest form, bi-linear elements, but you should
- be aware that higher order elements (bi-quadratic or bi-cubic spline elements)
+ We will stick to the simplest form, bilinear elements, but you should be
+ aware that higher order elements (biquadratic or bicubic spline elements)
are also popular with some people.
- I am condensing a lot of very useful material from Chapter 3 of Hughes'
- book into one lecture.
+ This section is condensing a lot of very useful material from Chapter 3
+ of Hughes' book into a short overview.
If you want to see more complete derivations, proofs of convergence, etc.,
of how to go about using higher order elements, look at Hughes book, Chapter
3.
\end_layout
\begin_layout Standard
-Lets start by thinking of a rectangle that is 2a by 2b in length centered
+Let's start by thinking of a rectangle that is 2a by 2b in length centered
at (0,0).
There are two properties we would like the shape functions to have
\begin_inset Formula \begin{eqnarray}
@@ -861,7 +911,7 @@
\end_inset
- Equation\InsetSpace ~
+Equation\InsetSpace ~
\begin_inset LatexCommand ref
reference "eq:normalize"
@@ -894,7 +944,7 @@
\end_inset
- these shape functions satisfy the conditions in Equation\InsetSpace ~
+these shape functions satisfy the conditions in Equation\InsetSpace ~
\begin_inset LatexCommand ref
reference "eq:normalize"
@@ -917,83 +967,62 @@
.
A good exercise would be to show this is true.
-\end_layout
-
-\begin_layout Quote
-
-\series bold
-Problem 7
-\series default
- Show that the shape functions defined above satisfy Equation\InsetSpace ~
-
+ A visual representation of these shape functions is shown in Figure
\begin_inset LatexCommand ref
-reference "eq:normalize"
+reference "fig:The-bilinear-shape"
\end_inset
- and Equations\InsetSpace ~
-
-\begin_inset LatexCommand ref
-reference "eq:interpx"
-
-\end_inset
-
- and\InsetSpace ~
-
-\begin_inset LatexCommand ref
-reference "eq:interpy"
-
-\end_inset
-
.
-
\end_layout
\begin_layout Standard
-Notice that by convention, I start numbering my element nodes in the lower
- left hand corner and work counter-clockwise.
-
-\begin_inset ERT
-status collapsed
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
\begin_layout Standard
+\begin_inset Caption
-{
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:The-bilinear-shape"
+
+\end_inset
+
+The bilinear shape function for a single element (top) and the four elements
+ whose shape functions combine to form the global shape function for node
+ A (bottom).
+ Figure taken from Hughes, Section 3.2.
\end_layout
\end_inset
-\begin_inset ERT
-status collapsed
+\end_layout
\begin_layout Standard
+\noindent
+\align center
+\begin_inset Graphics
+ filename images/conman-fig2.eps
+ scale 40
+\end_inset
-\backslash
-em
+
\end_layout
\end_inset
- This is a very important point.
- It is followed through out all my finite element codes.
-\begin_inset ERT
-status collapsed
-\begin_layout Standard
-
-}
\end_layout
-\end_inset
-
- There is no magic reason, you just have to choose a starting place.
-\end_layout
-
\begin_layout Standard
-In ConMan, as in Hughes, we further choose to normalize this by setting
-
+In ConMan we further choose to normalize this by setting
\begin_inset Formula $a=1$
\end_inset
@@ -1037,13 +1066,13 @@
What do we do if we want to solve a problem on a domain that is not convenient
to split into a grid of 1 by 1 unit elements? We use an important principle
- of mathematics, the jacobian of the transformation
+ of mathematics, the Jacobian of the transformation
\begin_inset Formula \begin{equation}
K_{11}~=~\int_{A}^{B}N_{1,x}N_{1,x}\, dx~=~\int_{0}^{1}N_{1,x}N_{1,x}\, Jdx\end{equation}
\end_inset
- where
+where
\begin_inset Formula $J$
\end_inset
@@ -1054,13 +1083,66 @@
\begin_inset Formula $a=b=1$
\end_inset
- above.
- However, if we are thinking about a cylindrical geometry, for example,
- we can use the Jacobian of the transformation between the geometries.
- Lets look at two examples:
+ above (see Figure
+\begin_inset LatexCommand ref
+reference "fig:Figure-1"
+
+\end_inset
+
+).
\end_layout
\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Figure-1"
+
+\end_inset
+
+The mapping between the global domain (right) and the parent element domain
+ (left) using the shape functions.
+ Figure taken from Hughes, Section 3.2.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Graphics
+ filename images/conman-fig1.eps
+ scale 45
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+However, if we are thinking about a cylindrical geometry, for example, we
+ can use the Jacobian of the transformation between the geometries.
+ Let's look at two examples:
+\end_layout
+
+\begin_layout Standard
Converting an element 0.05 by 0.10 centered at (0.1,0.2) to the `parent element'
centered at (0,0).
Hughes also uses
@@ -1071,7 +1153,7 @@
\begin_inset Formula $X,Y$
\end_inset
- coordinate pair in the `parent element' So we could write
+ coordinate pair in the `parent element.' So we could write
\begin_inset Formula \begin{eqnarray}
x & = & 0.1+{0.05}\xi+0.0\eta\\
y & = & 0.2+{0.0}\xi+{0.10}\eta\end{eqnarray}
@@ -1092,20 +1174,20 @@
\end_inset
- Where
+Where
\begin_inset Formula $[J]$
\end_inset
- is the Jacobian of the transformation.
- If the transformation were from an arbitratry shaped quadralateral to the
- parent element, then the off diagonal terms will not be zero.
+ is the Jacobian of the transformation, if the transformation was from an
+ arbitratry shaped quadrilateral to the parent element, then the off diagonal
+ terms will not be zero.
It is easy enough to show that
\begin_inset Formula \begin{equation}
\int_{x_{1}}^{x_{2}}\int_{y_{1}}^{y_{2}}f(x,y)\, dx\, dy=\int_{-1}^{1}\int_{-1}^{1}f(\xi,\eta)\,{\rm det}[J]\, d\xi\, d\eta\end{equation}
\end_inset
- It turns out, and it is also easy to show, that
+It turns out, and it is also easy to show, that
\begin_inset Formula ${\rm det}[J]$
\end_inset
@@ -1146,10 +1228,14 @@
\end_layout
\begin_layout Standard
-An amazing fact, that makes the idea of finite elements easy and powerful
+An amazing fact, that makes the idea of finite elements easy and powerful,
is Gauss Quadrature.
Gauss Quadrature is a way to turn an integral into a summation.
- Lets begin with a 1-D example, f(x) = c
+ Let's begin with a 1D example,
+\begin_inset Formula $f(x)=c$
+\end_inset
+
+
\begin_inset Formula \begin{equation}
\int_{-1}^{1}c\, dx=cx|_{-1}^{1}=2c\end{equation}
@@ -1161,7 +1247,11 @@
\end_inset
- For a linear function, f(x) = a x + b
+ For a linear function,
+\begin_inset Formula $f(x)=ax+b$
+\end_inset
+
+
\begin_inset Formula \begin{equation}
\int_{-1}^{1}f(x)\, dx=f(\frac{-1}{\sqrt{3}})+f(\frac{-1}{\sqrt{3}})\end{equation}
@@ -1179,7 +1269,7 @@
\end_inset
- It turns out that
+It turns out that
\begin_inset Formula $\frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}}$
\end_inset
@@ -1282,7 +1372,7 @@
Originally, we called this routine once and stored all the shape functions.
As problem sizes have grown, this took a lot of storage, so now we call
it on the fly for each element when needed.
- It is computationally more expensive but cuts storage.
+ It is computationally more expensive but cuts the storage requirement.
This strategy will also be necessary for a Lagrangian formulation or adaptive
gridding.
\end_layout
@@ -1311,50 +1401,6 @@
\end_layout
\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Caption
-
-\begin_layout Standard
-\begin_inset LatexCommand label
-name "fig:Figure-1"
-
-\end_inset
-
-The mapping between the global domain (right) and the parent element domain
- (left) using the shape functions.
- Figure taken from Hughes, Sec 3.2.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Graphics
- filename images/conman-fig1.eps
- scale 45
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
For ConMan the choice was made to use bilinear quadrilaterals as the parent
elements (Figure
\begin_inset LatexCommand ref
@@ -1371,67 +1417,47 @@
\end_layout
\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
+Because of the changing between domains, it is necessary to define several
+ bookkeeping arrays to identify nodes and elements in each of the domains.
+ It is worth noting that the numbering of local elements always begins with
+ 1 in the lower left-hand corner.
+ There is no special reason; you just have to choose a convention.
+\end_layout
-\begin_layout Standard
-\begin_inset Caption
+\begin_layout Description
+\begin_inset ERT
+status collapsed
\begin_layout Standard
-\begin_inset LatexCommand label
-name "fig:The-bilinear-shape"
-\end_inset
-
-The bilinear shape function for a single element (top) and the four elements
- whose shape functions combine to form the global shape function for node
- A (bottom).
- Figure taken from Hughes, Sec 3.2.
+{
\end_layout
\end_inset
-\end_layout
+\begin_inset ERT
+status collapsed
\begin_layout Standard
-\noindent
-\align center
-\begin_inset Graphics
- filename images/conman-fig2.png
- scale 40
-\end_inset
-
-
+{
\end_layout
\end_inset
-
-\end_layout
-
-\begin_layout Standard
-Because of the changing between domains, it is necessary to define several
- bookkeeping arrays to identify nodes and elements in each of the domains.
-\end_layout
-
-\begin_layout Description
+id
\begin_inset ERT
status collapsed
\begin_layout Standard
-{
+}
\end_layout
\end_inset
-id
+
\begin_inset ERT
status collapsed
@@ -1463,6 +1489,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ien
\begin_inset ERT
status collapsed
@@ -1474,6 +1511,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
transforms element local node numbers to global node numbers (Figure
\begin_inset LatexCommand ref
reference "fig:4-Example-relationship-between"
@@ -1495,6 +1543,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
lm
\begin_inset ERT
status collapsed
@@ -1506,6 +1565,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
transforms element local node numbers to global equation numbers.
\end_layout
@@ -1530,7 +1600,7 @@
Example relationship between global nodes and equation numbers for a 2
degree of freedom problem using the id array.
An equation number of zero denotes a boundary condition.
- Figure taken from Hughes, Sec 3.2.
+ Figure taken from Hughes, Section 3.2.
\end_layout
\end_inset
@@ -1589,8 +1659,8 @@
Example relationship between global node numbers and local element numbers
using the ien array.
- Local nodes are numbered counterclockwise from the bottom left hand corner.
- Figure taken from Hughes, Sec 3.2.
+ Local nodes are numbered counterclockwise from the bottom left-hand corner.
+ Figure taken from Hughes, Section 3.2.
\end_layout
\end_inset
@@ -1630,6 +1700,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
id
\begin_inset ERT
status collapsed
@@ -1641,6 +1722,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
( degree-of-freedom , global-node-number ) = equation-number
\end_layout
@@ -1655,6 +1747,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ien
\begin_inset ERT
status collapsed
@@ -1666,6 +1769,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
( local-node-number, element-number ) = global-node-number
\end_layout
@@ -1680,6 +1794,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
lm
\begin_inset ERT
status collapsed
@@ -1691,6 +1816,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
( degree-of-freedom, local-node-number, element-number ) = global-equation-numb
er
\end_layout
@@ -1702,15 +1838,16 @@
\begin_layout Standard
Transforming between the element and global points of view is done with
the data structure called the IEN array for Element to Node transformation.
- The IEN array takes an element number and a local node number and it's
+ The IEN array takes an element number and a local node number, and its
value is the global node number.
It is easiest to look at some examples:
\end_layout
\begin_layout Standard
-Consider a 3 element by 3 element grid.
- I will number my elements and node starting in the lower left hand corner,
- and working up fastest.
+Consider a 3-element by 3-element grid.
+ I will number my elements and nodes starting in the lower left hand corner,
+ and the node and element numbers will increase linearly in the vertical
+ direction.
\end_layout
\begin_layout Standard
@@ -1727,8 +1864,12 @@
\end_inset
For element 3: ien (3, 1) = 3 ien (3, 2) = 7 ien (3, 3) = 8 ien (3, 4)
- = 4 For element 5: ien (5, 1) = 6 ien (5, 2) = 10 ien (5, 3) = 11 ien (5,
- 4) = 7
+ = 4
+\end_layout
+
+\begin_layout Standard
+For element 5: ien (5, 1) = 6 ien (5, 2) = 10 ien (5, 3) = 11 ien (5, 4)
+ = 7
\begin_inset ERT
status collapsed
@@ -1745,10 +1886,10 @@
\end_layout
\begin_layout Standard
-There are three kinds of opperations we might think of wanting.
- The first is taking values of some function (coordinates, velocities, temperatu
-res, stresses, etc.) defined on the global grid and getting the values for
- a single element, this is called a
+There are three kinds of operations we might want to use.
+ The first is taking the values of some function (coordinates, velocities,
+ temperatures, stresses, etc.) defined on the global grid and getting the
+ values for a single element, which is called a
\begin_inset ERT
status collapsed
@@ -1785,7 +1926,7 @@
operation.
The next is taking values in an element and spreading them out to the global
- array, this is called a
+ array, which is called a
\begin_inset ERT
status collapsed
@@ -1861,10 +2002,17 @@
\end_layout
\begin_layout Standard
-All three operations, gather, scatter, and assemble are done by the routine
- local.
- Because it is called by the genshp routine above, it is a good example
- to look at.
+All three operations -- gather, scatter, and assemble -- are done by the
+ routine
+\series bold
+local
+\series default
+.
+ Because it is called by the
+\series bold
+genshp
+\series default
+ routine above, it is a good example to study.
\end_layout
\begin_layout Subsection
@@ -1890,7 +2038,7 @@
\end_inset
- We replace equation\InsetSpace ~
+ We replace Equation\InsetSpace ~
\begin_inset LatexCommand ref
reference "eq:constit"
@@ -1904,7 +2052,7 @@
\end_inset
- As
+As
\begin_inset Formula $\lambda$
\end_inset
@@ -1961,7 +2109,7 @@
\end_inset
- from Equation\InsetSpace ~
+from Equation\InsetSpace ~
\begin_inset LatexCommand ref
reference "eq:constit-lam2"
@@ -2007,7 +2155,7 @@
\end_inset
At this point, it is probably easier to switch to differential notation.
- I will also specialize to 2-D:
+ These will also specialize to 2D:
\begin_inset Formula \begin{eqnarray}
\frac{\partial}{\partial x}\{\lambda(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial z})+2\mu(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial x})/2\}+\frac{\partial}{\partial z}\{2\mu(\frac{\partial v}{\partial x}+\frac{\partial u}{\partial z})/2\}+f_{x}=0\\
\frac{\partial}{\partial x}\{2\mu(\frac{\partial u}{\partial z}+\frac{\partial v}{\partial x})/2\}+\frac{\partial}{\partial z}\{\lambda(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial z})+2\mu(\frac{\partial v}{\partial z}+\frac{\partial v}{\partial z})/2\}+f_{z}=0\end{eqnarray}
@@ -2019,7 +2167,7 @@
\begin_layout Standard
These are second order partial differential equations.
- Simplifying, I get
+ Simplifying, we get
\begin_inset Formula \begin{eqnarray}
\lambda(\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}v}{\partial x\partial z})+2\mu\frac{\partial^{2}u}{\partial x^{2}}+\mu(\frac{\partial^{2}u}{\partial z^{2}}+\frac{\partial^{2}v}{\partial z\partial x})+f_{x}=0\\
\lambda(\frac{\partial^{2}u}{\partial z\partial x}+\frac{\partial^{2}v}{\partial z^{2}})+\mu(\frac{\partial^{2}u}{\partial x\partial z}+\frac{\partial^{2}v}{\partial x^{2}})+2\mu\frac{\partial^{2}v}{\partial z^{2}}+f_{z}=0\end{eqnarray}
@@ -2032,7 +2180,7 @@
\begin_layout Standard
Now we use the same technique (approach) as we used in Possion's equation
to turn the differential form into an integral form.
- You can either look at it as we find the variational form of the stokes
+ You can either look at it as we find the variational form of the Stokes
equation (which is what we are doing) or you can think of it as multiplying
by a weighting function
\begin_inset Formula $w$
@@ -2041,10 +2189,13 @@
and integrating over the domain.
Then using integration by parts to convert the second derivatives to first
derivatives.
- This is done in carefully by Hughes on pages 197-200, but he has left out
- a number of intermediate steps.
- Nothing about this step is hard, it is just tedious.
- There is, however, a cleaver short cut.
+ This is done carefully by Hughes in
+\emph on
+The Finite Element Method
+\emph default
+ on pages 197-200, but he has left out a number of intermediate steps.
+ Nothing about this step is hard, just tedious.
+ There is, however, a clever shortcut.
If we return to the messy equations at the top of the page, multiply them
by the weighting function
\begin_inset Formula $w$
@@ -2052,12 +2203,12 @@
and integrate over the domain, then we do not have to use integration by
parts.
- If you are confused, or don't believe me, then you should take the equations
- directly above this paragraph, multiply by a weighting function
+ To see this for yourself, simply take the equations directly above this
+ paragraph, multiply by a weighting function
\begin_inset Formula $w$
\end_inset
- and integrate over the 2-D domain
+ and integrate over the 2D domain
\begin_inset Formula $\Omega$
\end_inset
@@ -2074,7 +2225,7 @@
\end_inset
- Note that we don't get something for nothing, this short cut does not give
+Note that we don't get something for nothing; this shortcut does not give
us the boundary condition terms (velocity or flux).
These would fall out of the integration by parts.
Recall,
@@ -2083,7 +2234,7 @@
\end_inset
- were in our case
+where in our case
\begin_inset Formula $w$
\end_inset
@@ -2136,7 +2287,7 @@
\end_inset
part.
- We can also write them as a 2-D matrix equation
+ We can also write them as a 2D matrix equation
\begin_inset Formula \begin{equation}
[K_{\lambda}]=\left[\begin{array}{cc}
N_{x}\lambda N_{x} & N_{x}\lambda N_{z}\\
@@ -2156,12 +2307,12 @@
\end_layout
\begin_layout Standard
-Hughes makes use of an interesting, and important observation.
+Hughes makes use of an interesting and important observation.
This observation will greatly simplify constructing the stiffness matrix
for arbitrary coordinate systems.
We can rewrite the stiffness matrices above in the following form:
\begin_inset Formula \begin{equation}
-[K_{\lambda}]+[K_{\mu}]=[B]^{T}[D][B]\end{equation}
+[K_{\lambda}]+[K_{\mu}]=[B]^{T}[D][B]\label{eq:84}\end{equation}
\end_inset
@@ -2222,13 +2373,25 @@
\end_layout
\begin_layout Standard
-The element stiffness matrix (Figure
+The element stiffness matrix (Equation\InsetSpace ~
+
\begin_inset LatexCommand ref
-reference "fig:5-The-element-stiffness"
+reference "eq:84"
\end_inset
) is made up of the two terms from the left hand side of the integral equation.
+ The full element stiffness matrix for the quadralilateral element is an
+ 8 by 8 matrix made up of 16 of the 2 by 2 matrices as shown in Figure\InsetSpace ~
+
+\begin_inset LatexCommand ref
+reference "fig:8-The-storage-for"
+
+\end_inset
+
+.
+ Because of symmetry we only need to form and store the upper triangular
+ part of the matrix.
The integration is done using two by two gauss quadrature, which is exact
when the elements are rectangular and bilinear shape functions are used.
The
@@ -2236,29 +2399,46 @@
\end_inset
term is under-integrated (one point rule) to keep the large penalty value
- from effectively locking the element (Malkus and Hughes, 1978).
- The right hand side is made up of three known parts, the body force term
- (
+ from effectively locking the element
+\begin_inset LatexCommand cite
+key "Malkus and Hughes 1978"
+
+\end_inset
+
+.
+ The right-hand side is made up of three known parts, the body force term
+ (
\begin_inset Formula $f_{i}$
\end_inset
- ), the applied tractions (
+), the applied tractions (
\begin_inset Formula $h_{i}$
\end_inset
- ) and the applied velocities (
+) and the applied velocities (
\begin_inset Formula $g_{i}$
\end_inset
- ).
+).
The momentum equation is equivalent to an incompressible elastic problem,
- and the resulting stiffness matrix will always be positive definite (Hughes,
- 1986 p.
- 84-89).
+ and the resulting stiffness matrix will always be positive definite
+\begin_inset LatexCommand cite
+after "p. 84-89"
+key "Hughes 1987"
+
+\end_inset
+
+.
This allows us to consider only the upper triangular part of the stiffness
matrix and save both storage and operations using Cholesky factorization.
More details of the method and a formal error analysis can be found in
- Hughes, Liu and Brooks (1979).
+
+\begin_inset LatexCommand cite
+key "Hughes et al 1979"
+
+\end_inset
+
+.
\end_layout
\begin_layout Standard
@@ -2266,7 +2446,7 @@
\series bold
f_vstf
\series default
- and the right hand side is formed in routine
+ and the right-hand side is formed in routine
\series bold
f_tres
\series default
@@ -2274,63 +2454,221 @@
\end_layout
\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
+\begin_inset ERT
+status collapsed
\begin_layout Standard
-\begin_inset Caption
+%
+\backslash
+noindent
+\backslash
+begin{center}
+\end_layout
+
\begin_layout Standard
-\begin_inset LatexCommand label
-name "fig:5-The-element-stiffness"
+\end_layout
+
\end_inset
-The element stiffness matrix for the 2D Cartesian stokes equation.
- The 8 by 8 matrix is make up of 16 2 by 2 submatrices of the form shown
- below.
- The
-\begin_inset Formula $\lambda$
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%
+\backslash
+begin{figure}
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
\end_inset
- and
-\begin_inset Formula $\mu$
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%
+\backslash
+caption{
+\backslash
+label{fig:5-The-element-stiffness}The element stiffness matrix for
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
\end_inset
- parts are shown separately for clarity.
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%the 2D Cartesian stokes equation.
+ The 8 by 8 matrix is make up of
\end_layout
+\begin_layout Standard
+
+\end_layout
+
\end_inset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%16 2 by 2 submatrices of the form shown below.
+ The $
+\backslash
+lambda$ and
\end_layout
\begin_layout Standard
-\noindent
-\align center
-\begin_inset Graphics
- filename images/conman-fig5.eps
- scale 40
+\end_layout
+
\end_inset
-
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%$
+\backslash
+mu$ parts are shown separately for clarity.}
\end_layout
+\begin_layout Standard
+
+\end_layout
+
\end_inset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%
+\backslash
+noindent
+\backslash
+begin{centering}
\end_layout
\begin_layout Standard
-I'm not sure if we need this too...
+
\end_layout
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
\begin_layout Standard
+
+%
+\backslash
+includegraphics[scale=0.4]{images/conman-fig5}
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%
+\backslash
+par
+\backslash
+end{centering}
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%
+\backslash
+end{figure}
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%
+\backslash
+par
+\backslash
+end{center}
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Standard
+
+%I'm not sure if we need this too...
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
\noindent
\align center
\begin_inset Float figure
@@ -2416,6 +2754,7 @@
\end_layout
\begin_layout Standard
+\noindent
where
\begin_inset Formula $T$
\end_inset
@@ -2455,6 +2794,7 @@
\end_layout
\begin_layout Standard
+\noindent
where
\begin_inset Formula $\dot{T}$
\end_inset
@@ -2488,7 +2828,13 @@
The energy equation is solved using Petrov-Galerkin weighting functions
on the internal heat source and advective terms to correct for the under-diffus
ion and remove the oscillations which would result from the standard Galerkin
- method for an advection dominated problem (Hughes and Brooks, 1977).
+ method for an advection dominated problem
+\begin_inset LatexCommand cite
+key "Hughes and Brooks 1979"
+
+\end_inset
+
+.
The Petrov-Galerkin function can be thought of as a standard Galerkin method
in which we counterbalance the numerical underdiffusion by adding an artificial
diffusivity of the form
@@ -2504,6 +2850,7 @@
\end_layout
\begin_layout Standard
+\noindent
with
\end_layout
@@ -2526,6 +2873,7 @@
\end_layout
\begin_layout Standard
+\noindent
where
\begin_inset Formula $h_{\xi}$
\end_inset
@@ -2551,22 +2899,27 @@
\end_inset
system) evaluated at the element center.
- This form of discretization has no crosswind diffusion because the
-\begin_inset Quotes eld
-\end_inset
+ This form of discretization has no crosswind diffusion because the ``artificial
+ diffusion'' acts only in the direction of the flow (i.e., it follows the
+ streamline), hence the name Streamline Upwind Petrov-Galerkin (SUPG).
+ This makes it a better approximation than straight upwinding, and it has
+ been demonstrated to be more accurate than Galerkin or straight upwinding
+ in advection dominated problems
+\begin_inset LatexCommand cite
+key "Hughes and Brooks 1979"
-artificial diffusion
-\begin_inset Quotes erd
\end_inset
- acts only in the direction of the flow (i.e., it follows the streamline),
- hence the name Streamline Upwind Petrov-Galerkin (SUPG).
- This makes it a better approximation than straight upwinding and it has
- been demonstrated to be more accurate than Galerkin or straight upwinding
- in advection dominated problems (Hughes and Brooks, 1977).
+.
It has recently been shown that the SUPG method is one of a broader class
of methods for advection-diffusion equations referred to as Galerkin/Least-Squa
-res methods (Hughes et al., 1988).
+res methods
+\begin_inset LatexCommand cite
+key "Hughes et al 1988"
+
+\end_inset
+
+.
\end_layout
\begin_layout Standard
@@ -2579,7 +2932,13 @@
The added cost of calculating the Petrov-Galerkin weighting functions is
much less than the cost of using a refined grid with the Galerkin method.
The Galerkin method requires a finer grid then the Petrov-Galerkin method
- to achieve stable solutions (Travis et al., 1989).
+ to achieve stable solutions
+\begin_inset LatexCommand cite
+key "Travis et al 1990"
+
+\end_inset
+
+.
Time stepping in the energy equation is done using an explicit predictor-correc
tor algorithm.
The form of the predictor-corrector algorithm is
@@ -2661,6 +3020,7 @@
\end_layout
\begin_layout Standard
+\noindent
where
\begin_inset Formula $i$
\end_inset
@@ -2669,7 +3029,7 @@
\begin_inset Formula $n$
\end_inset
- is the time step number,
+ is the time-step number,
\begin_inset Formula $T$
\end_inset
@@ -2712,9 +3072,14 @@
\begin_inset Formula $\alpha$
\end_inset
- = 0.5 and two iterations, the method is second order accurate (Hughes, 1986,
- p.
- 562-566).
+ = 0.5 and two iterations, the method is second order accurate
+\begin_inset LatexCommand cite
+after "p. 562-566"
+key "Hughes 1987"
+
+\end_inset
+
+.
\end_layout
\begin_layout Standard
@@ -2782,8 +3147,8 @@
\end_layout
\begin_layout Standard
-There are three significant differences that the user who has seen versions
- of ConMan in the past will find in this version.
+There are three significant differences that the user familiar with past
+ versions of ConMan will find in this version.
The original version of ConMan, distributed by King and/or Hager, was designed
to take advantage of machines with vector registers, such as the Cray X-MP
or Y-MP.
@@ -2793,10 +3158,10 @@
\end_layout
\begin_layout Standard
-With this version of ConMan, the reordering of elements into block with
- independent degrees of freedom and the reorganization of routines into
- loops over element groups with inner do-loops having lengths equal to the
- length of vector registers has been removed.
+In this version of ConMan, the reordering of elements into blocks with independe
+nt degrees of freedom and the reorganization of routines into loops over
+ element groups with inner do-loops having lengths equal to the length of
+ vector registers has been removed.
This means that the structure of the routines that form the element stiffness
matrix (
\series bold
@@ -2812,8 +3177,8 @@
f_tmres.F
\series default
) are now loops over elements with short inner loops over local element
- nodes and or integration points.
- One could argue that because modern CPU's relying on fast cache to keep
+ nodes and/or integration points.
+ One could argue that because modern CPU is relying on fast cache to keep
the arithmatic units busy, the kind of grouping we did to take advantage
of vector registers is still useful for modern processors.
However, the element reordering made algorithms such as particle tracking
@@ -2825,7 +3190,12 @@
\begin_layout Standard
The second major change is that we have implemented a Picard iteration algorithm
for steady-state problems (c.f.
- van Keken - thesis).
+ van Keken - thesis
+\series bold
+[TODO: This sounds different from the van Keken bib entry we have now.
+ What thesis?]
+\series default
+).
Currently, this is implemented by changing compiler flags in the Makefile.
Picard iteration is an implicit solution to the energy equation (as opposed
to the predictor-corrector method described above); hence, non-symmetric
@@ -2841,14 +3211,14 @@
in the Time Sequence card (second line of the input file) from 0.5 to 1.0
and change the iterations from 2 to 1 (same line).
- You need to "make clean" and remake with the target picard, to generate
+ You need to ``make clean'' and remake with the target Picard, to generate
a new executable (conman.pic).
A future revision may merge these energy equation solvers into a single
code and hide the need to change the iteration steps from the user.
When you have a steady-state solution, Picard iteration usually converges
in 10-100 steps, as opposed to several thousand steps.
- When there is no steady solution, the Picard results are not useful and
- the explicit solver should be used.
+ When there is no steady-state solution, the Picard results are not useful
+ and the explicit solver should be used.
\end_layout
\begin_layout Standard
@@ -2898,17 +3268,38 @@
\end_inset
call.
- The reason for this change is fairly technical, and I will spare the users
- with the details.
- The memory manager source can be found in the directory mm.src.
+ The reason for this change is fairly technical, and I will spare the user
+ the details.
+ The memory manager source can be found in the directory
+\family typewriter
+mm.src
+\family default
+.
Care has to be taken when compiling on 32-bit or 64-bit machines (change
- the header file in mm.src from mm2000_32.h to mm2000_64.h) and change the
- compile flags in the Makefile.
+ the header file in
+\family typewriter
+mm.src
+\family default
+ from
+\family typewriter
+mm2000_32.h
+\family default
+ to
+\family typewriter
+mm2000_64.h
+\family default
+) and change the compile flags in the Makefile.
It is now possible to use Fortran90's allocate routine for dynamic memory
- allocation and the memory manager should be removed in a future revision.
+ allocation, and the memory manager should be removed in a future revision.
Making changes in the memory manager is tricky and this package is fragile.
- Users who have a problem with the memory manager should consult CIG or
- Scott King.
+ Users who have a problem with the memory manager should request assistance
+ by contacting the CIG Mantle Convection Mailing List
+\begin_inset LatexCommand url
+target "cig-mc at geodynamics.org"
+
+\end_inset
+
+.
\end_layout
\begin_layout Section
@@ -3059,7 +3450,7 @@
\begin_inset Formula $E^{*}$
\end_inset
-, is input as Tcon(1)
+ is input as Tcon(1),
\begin_inset Formula $V^{*}$
\end_inset
@@ -3072,7 +3463,7 @@
rheol.newt.F
\series default
to be 273.
- and
+
\begin_inset Formula $\Delta T$
\end_inset
@@ -3101,7 +3492,7 @@
\begin_layout Standard
Internal heating can be specified through the internal heating parameter.
- If no bottom temperature is specified the Rayleigh number becomes
+ If no bottom temperature is specified, the Rayleigh number becomes
\end_layout
\begin_layout Standard
@@ -3152,7 +3543,7 @@
\end_layout
\begin_layout Section
-Building from Source [WEI -- thought you might need this section.
+Building from Source [TODO WEI -- thought you might need this section.
Or else delete]
\end_layout
@@ -3374,8 +3765,8 @@
\series default
, contains the coordinates, boundary values and connectivity information.
ConMan reads the file names to attach to these units from standard input.
- The typical way to run conman is to create a file with nine lines, one
- file name per line and redirect this into the executable (i.e., % conman.pic
+ The typical way to run ConMan is to create a file with nine lines, one
+ file name per line, and redirect this into the executable (i.e., % conman.pic
< runfile & ).
\series bold
@@ -3393,7 +3784,7 @@
The input deck was broken up so that an automatic grid generating routine
could be used to generate coordinates, boundary conditions and element
connectivities separate from ConMan.
- The only automatic grid generation conman does is linear or bilinear interpolat
+ The only automatic grid generation ConMan does is linear or bilinear interpolat
ion which is described in the appropriate sections of this guide.
\end_layout
@@ -3402,24 +3793,10 @@
\series bold
iin
\series default
- unit (throughout this guide a
-\begin_inset Quotes eld
-\end_inset
-
-card
-\begin_inset Quotes erd
-\end_inset
-
- will mean one line of an ASCII text file).
- These constitute the parameter part of the input
-\begin_inset Quotes eld
-\end_inset
-
-deck
-\begin_inset Quotes erd
-\end_inset
-
- for the program ConMan.
+ unit (throughout this guide a ``card'' will mean one line of an ASCII text
+ file).
+ These constitute the parameter part of the input ``deck'' for the program
+ ConMan.
The format for this guide is a
\series bold
bold
@@ -3443,6 +3820,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Title\InsetSpace ~
Card
\begin_inset ERT
@@ -3455,6 +3843,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
Any descriptive character string up to 80 characters long
@@ -3473,6 +3872,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Global\InsetSpace ~
Constants\InsetSpace ~
Card
@@ -3486,12 +3896,21 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
numnp nsd ndof nelx nelz mprec iflow necho inrsts iorstr nodebn ntimvs ntseq
numeg isky nwrap
-\emph default
-
\end_layout
\begin_deeper
@@ -3506,6 +3925,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
numnp
\begin_inset ERT
status collapsed
@@ -3517,6 +3947,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -3537,6 +3978,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nsd
\begin_inset ERT
status collapsed
@@ -3548,6 +4000,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -3570,6 +4033,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ndof
\begin_inset ERT
status collapsed
@@ -3581,6 +4055,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -3602,6 +4087,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nelx
\begin_inset ERT
status collapsed
@@ -3613,6 +4109,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -3634,6 +4141,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nelz
\begin_inset ERT
status collapsed
@@ -3645,6 +4163,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -3666,6 +4195,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
mprec
\begin_inset ERT
status collapsed
@@ -3677,6 +4217,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -3707,6 +4258,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
iflow
\begin_inset ERT
status collapsed
@@ -3718,6 +4280,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
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.
.
.
@@ -3749,6 +4322,17 @@
\end_inset
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+
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necho
\begin_inset ERT
status collapsed
@@ -3760,6 +4344,17 @@
\end_inset
+
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+
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+}
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.
.
.
@@ -3790,6 +4385,17 @@
\end_inset
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+
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+{
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+
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inrstr
\begin_inset ERT
status collapsed
@@ -3801,6 +4407,17 @@
\end_inset
+
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+}
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.
.
.
@@ -3832,6 +4449,17 @@
\end_inset
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+
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iorstr
\begin_inset ERT
status collapsed
@@ -3843,6 +4471,17 @@
\end_inset
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+}
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.
.
.
@@ -3898,6 +4537,17 @@
\end_inset
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+
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+
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nodebn
\begin_inset ERT
status collapsed
@@ -3909,6 +4559,17 @@
\end_inset
+
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+}
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.
.
.
@@ -3929,6 +4590,17 @@
\end_inset
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+
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+
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ntimvs
\begin_inset ERT
status collapsed
@@ -3940,6 +4612,17 @@
\end_inset
+
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+}
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.
.
.
@@ -3970,6 +4653,17 @@
\end_inset
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ntseq
\begin_inset ERT
status collapsed
@@ -3981,6 +4675,17 @@
\end_inset
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+
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+}
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.
.
.
@@ -4008,6 +4713,17 @@
\end_inset
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+
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numeg
\begin_inset ERT
status collapsed
@@ -4019,6 +4735,17 @@
\end_inset
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+}
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.
.
.
@@ -4045,6 +4772,17 @@
\end_inset
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isky
\begin_inset ERT
status collapsed
@@ -4056,6 +4794,17 @@
\end_inset
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+}
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.
.
.
@@ -4087,6 +4836,17 @@
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nwrap
\begin_inset ERT
status collapsed
@@ -4098,6 +4858,17 @@
\end_inset
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+}
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.
.
.
@@ -4133,6 +4904,17 @@
\end_inset
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Time\InsetSpace ~
Sequence\InsetSpace ~
Cards
@@ -4146,6 +4928,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
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+}
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+
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+
- ntseq cards
\end_layout
@@ -4154,8 +4947,6 @@
\emph on
nstep niter alpha delt epstol
-\emph default
-
\end_layout
\begin_layout Description
@@ -4169,6 +4960,17 @@
\end_inset
+
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+status collapsed
+
+\begin_layout Standard
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+{
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+
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nstep
\begin_inset ERT
status collapsed
@@ -4180,6 +4982,17 @@
\end_inset
+
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+status collapsed
+
+\begin_layout Standard
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+}
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+
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.
.
.
@@ -4187,7 +5000,7 @@
.
.
.
- number of time steps
+ number of time steps
\end_layout
\begin_layout Description
@@ -4201,6 +5014,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
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+{
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+
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+
niter
\begin_inset ERT
status collapsed
@@ -4212,6 +5036,17 @@
\end_inset
+
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+
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+}
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+
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.
.
.
@@ -4243,6 +5078,17 @@
\end_inset
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+{
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+
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alpha
\begin_inset ERT
status collapsed
@@ -4254,6 +5100,17 @@
\end_inset
+
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+
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+}
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.
.
.
@@ -4285,6 +5142,17 @@
\end_inset
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+{
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+
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+
delt
\begin_inset ERT
status collapsed
@@ -4296,6 +5164,17 @@
\end_inset
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+}
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.
.
.
@@ -4317,6 +5196,17 @@
\end_inset
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+{
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epstol
\begin_inset ERT
status collapsed
@@ -4328,6 +5218,17 @@
\end_inset
+
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+
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+}
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.
.
.
@@ -4349,6 +5250,17 @@
\end_inset
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Output\InsetSpace ~
Step\InsetSpace ~
Card
@@ -4362,11 +5274,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
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+}
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+
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\emph on
nsdprt nsvprt nstprt nsmprt
-\emph default
-
\end_layout
\begin_deeper
@@ -4381,6 +5302,17 @@
\end_inset
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+
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+{
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nsdprt
\begin_inset ERT
status collapsed
@@ -4392,6 +5324,17 @@
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+}
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.
.
.
@@ -4412,6 +5355,17 @@
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nsvprt
\begin_inset ERT
status collapsed
@@ -4423,6 +5377,17 @@
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+}
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.
.
.
@@ -4443,6 +5408,17 @@
\end_inset
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nstprt
\begin_inset ERT
status collapsed
@@ -4454,6 +5430,17 @@
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+}
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.
.
.
@@ -4474,6 +5461,17 @@
\end_inset
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nsmprt
\begin_inset ERT
status collapsed
@@ -4485,6 +5483,17 @@
\end_inset
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+}
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.
.
.
@@ -4506,6 +5515,17 @@
\end_inset
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Velocity\InsetSpace ~
Boundary\InsetSpace ~
Condition\InsetSpace ~
@@ -4521,11 +5541,20 @@
\end_inset
+
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+status collapsed
+
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+}
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+
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\emph on
bnode enode incr (bcf(i), i=1,ndof)
-\emph default
-
\end_layout
\begin_deeper
@@ -4540,6 +5569,17 @@
\end_inset
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bnode
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status collapsed
@@ -4551,6 +5591,17 @@
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+}
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.
.
.
@@ -4571,6 +5622,17 @@
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enode
\begin_inset ERT
status collapsed
@@ -4582,6 +5644,17 @@
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+}
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.
.
.
@@ -4602,6 +5675,17 @@
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incr
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status collapsed
@@ -4613,6 +5697,17 @@
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+}
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.
.
.
@@ -4634,6 +5729,17 @@
\end_inset
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bcf(i)
\begin_inset ERT
status collapsed
@@ -4645,6 +5751,17 @@
\end_inset
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+}
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.
.
.
@@ -4670,8 +5787,6 @@
\emph on
0 0 0 0 0 to end VBCF cards
-\emph default
-
\end_layout
\begin_layout Description
@@ -4685,6 +5800,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
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Temperature\InsetSpace ~
Boundary\InsetSpace ~
Condition\InsetSpace ~
@@ -4700,11 +5826,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
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+}
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\emph on
bnode enode incr bcf
-\emph default
-
\end_layout
\begin_deeper
@@ -4719,6 +5854,17 @@
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bnode
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status collapsed
@@ -4730,6 +5876,17 @@
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+}
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.
.
.
@@ -4750,6 +5907,17 @@
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enode
\begin_inset ERT
status collapsed
@@ -4761,6 +5929,17 @@
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+}
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.
.
.
@@ -4781,6 +5960,17 @@
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incr
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status collapsed
@@ -4792,6 +5982,17 @@
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+}
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.
.
.
@@ -4813,6 +6014,17 @@
\end_inset
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bcf
\begin_inset ERT
status collapsed
@@ -4824,6 +6036,17 @@
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+}
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.
.
.
@@ -4845,8 +6068,6 @@
\emph on
0 0 0 0 to end TBCF cards
-\emph default
-
\end_layout
\end_deeper
@@ -4861,6 +6082,17 @@
\end_inset
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+\begin_inset ERT
+status collapsed
+
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+{
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Nusselt\InsetSpace ~
Number\InsetSpace ~
Boundary\InsetSpace ~
@@ -4880,11 +6112,20 @@
\end_inset
+
+\begin_inset ERT
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+}
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top and bottom rows of nodes
\emph on
bnode enode incr
-\emph default
-
\end_layout
\begin_deeper
@@ -4899,6 +6140,17 @@
\end_inset
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+{
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bnode
\begin_inset ERT
status collapsed
@@ -4910,6 +6162,17 @@
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+}
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.
.
.
@@ -4930,6 +6193,17 @@
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enode
\begin_inset ERT
status collapsed
@@ -4941,6 +6215,17 @@
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+}
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.
.
.
@@ -4961,6 +6246,17 @@
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incr
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status collapsed
@@ -4972,6 +6268,17 @@
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+}
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.
.
.
@@ -5000,6 +6307,17 @@
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Nusselt\InsetSpace ~
Number\InsetSpace ~
Boundary\InsetSpace ~
@@ -5020,11 +6338,20 @@
\end_inset
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+}
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second from top and bottom rows of nodes
\emph on
bnode enode incr
-\emph default
-
\end_layout
\begin_deeper
@@ -5039,6 +6366,17 @@
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bnode
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status collapsed
@@ -5050,6 +6388,17 @@
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+}
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.
.
.
@@ -5070,6 +6419,17 @@
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enode
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status collapsed
@@ -5081,6 +6441,17 @@
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+}
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.
.
.
@@ -5101,6 +6472,17 @@
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incr
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status collapsed
@@ -5112,6 +6494,17 @@
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+}
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.
.
.
@@ -5140,6 +6533,17 @@
\end_inset
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+{
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Initial\InsetSpace ~
Temperature\InsetSpace ~
Card
@@ -5153,6 +6557,17 @@
\end_inset
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+status collapsed
+
+\begin_layout Standard
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+}
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+
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\emph on
pert xsize zsize
@@ -5170,6 +6585,17 @@
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+status collapsed
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+{
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pert
\begin_inset ERT
status collapsed
@@ -5181,6 +6607,17 @@
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+}
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.
.
.
@@ -5202,6 +6639,17 @@
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xsize
\begin_inset ERT
status collapsed
@@ -5213,6 +6661,17 @@
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+}
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.
.
.
@@ -5234,6 +6693,17 @@
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zsize
\begin_inset ERT
status collapsed
@@ -5245,6 +6715,17 @@
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+}
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.
.
.
@@ -5267,6 +6748,17 @@
\end_inset
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+
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Element\InsetSpace ~
Parameter\InsetSpace ~
Cards
@@ -5280,11 +6772,20 @@
\end_inset
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+status collapsed
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+}
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- numeg cards
\emph on
ntype numel nen nenl numat nedof numsuf nipt implv implt
-\emph default
-
\end_layout
\begin_deeper
@@ -5299,6 +6800,17 @@
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ntype
\begin_inset ERT
status collapsed
@@ -5310,6 +6822,17 @@
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+}
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.
.
.
@@ -5337,6 +6860,17 @@
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numel
\begin_inset ERT
status collapsed
@@ -5348,6 +6882,17 @@
\end_inset
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+}
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.
.
.
@@ -5368,6 +6913,17 @@
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nen
\begin_inset ERT
status collapsed
@@ -5379,6 +6935,17 @@
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+}
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.
.
.
@@ -5401,6 +6968,17 @@
\end_inset
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+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nenl
\begin_inset ERT
status collapsed
@@ -5412,6 +6990,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5433,6 +7022,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
numat
\begin_inset ERT
status collapsed
@@ -5444,6 +7044,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5464,6 +7075,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nedof
\begin_inset ERT
status collapsed
@@ -5475,6 +7097,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5496,6 +7129,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
numsuf
\begin_inset ERT
status collapsed
@@ -5507,6 +7151,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5527,6 +7182,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nipt
\begin_inset ERT
status collapsed
@@ -5538,6 +7204,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5559,6 +7236,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
implv
\begin_inset ERT
status collapsed
@@ -5570,6 +7258,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5591,6 +7290,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
implt
\begin_inset ERT
status collapsed
@@ -5602,6 +7312,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5624,6 +7345,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Viscosity\InsetSpace ~
Card
\begin_inset ERT
@@ -5636,11 +7368,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
visc(i), i=1,numat
-\emph default
-
\end_layout
\begin_deeper
@@ -5655,6 +7396,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
visc(i)
\begin_inset ERT
status collapsed
@@ -5666,6 +7418,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5687,6 +7450,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Penalty\InsetSpace ~
Card
\begin_inset ERT
@@ -5699,11 +7473,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
alam(i), i=1,numat
-\emph default
-
\end_layout
\begin_deeper
@@ -5718,6 +7501,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
alam(i)
\begin_inset ERT
status collapsed
@@ -5729,6 +7523,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5750,6 +7555,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Diffusivity\InsetSpace ~
Card
\begin_inset ERT
@@ -5762,6 +7578,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
diff(i), i=1,numat
@@ -5779,6 +7606,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
diff(i)
\begin_inset ERT
status collapsed
@@ -5790,6 +7628,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5812,6 +7661,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Buoyancy\InsetSpace ~
Rayleigh\InsetSpace ~
Number\InsetSpace ~
@@ -5826,11 +7686,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
Ra(i), i=1,numat
-\emph default
-
\end_layout
\begin_deeper
@@ -5845,6 +7714,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Ra(i)
\begin_inset ERT
status collapsed
@@ -5856,6 +7736,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5878,6 +7769,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Internal\InsetSpace ~
Heating\InsetSpace ~
Parameter\InsetSpace ~
@@ -5892,11 +7794,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
dmhu(i), i=1,numat
-\emph default
-
\end_layout
\begin_deeper
@@ -5911,6 +7822,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
dmhu(i)
\begin_inset ERT
status collapsed
@@ -5922,6 +7844,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -5943,6 +7876,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Activation\InsetSpace ~
Energy\InsetSpace ~
Card
@@ -5956,9 +7900,22 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
tcon(1,i), i=1,numat
+\emph default
+
\end_layout
\begin_deeper
@@ -5973,6 +7930,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
tcon(1,i)
\begin_inset ERT
status collapsed
@@ -5984,13 +7952,24 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
.
.
- nondimensional activation energy for ith material group for temperature
- dependent viscosity
+ activation energy for ith material group for temperature dependent viscosity
+ (kJ/mole)
\end_layout
\end_deeper
@@ -6005,11 +7984,19 @@
\end_inset
-Temperature\InsetSpace ~
-Dependent\InsetSpace ~
-Viscosity\InsetSpace ~
-Temperature\InsetSpace ~
-Offset\InsetSpace ~
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+Activation\InsetSpace ~
+Volume\InsetSpace ~
Card
\begin_inset ERT
status collapsed
@@ -6021,6 +8008,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
tcon(2,i), i=1,numat
@@ -6038,6 +8036,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
tcon(2,i)
\begin_inset ERT
status collapsed
@@ -6049,13 +8058,28 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
.
.
- nondimen temperature offset for ith material group for temperature dependent
- viscosity
+ activation volume for ith material group for temperature dependent viscosity
+ (cm
+\begin_inset Formula $^{3}$
+\end_inset
+
+/mole)
\end_layout
\end_deeper
@@ -6070,6 +8094,122 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+Viscosity\InsetSpace ~
+Cutoff\InsetSpace ~
+Card
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\emph on
+tcon(3,i), i=1,numat
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+tcon(3,i)
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ .
+ .
+ .
+ .
+ .
+ maximum value of the viscosity for the ith material group
+\end_layout
+
+\end_deeper
+\begin_layout Description
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Surface\InsetSpace ~
Force/Flux\InsetSpace ~
Cards
@@ -6083,11 +8223,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
- numsuf cards
\emph on
nel side fnorm ftan flux
-\emph default
-
\end_layout
\begin_deeper
@@ -6102,6 +8251,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nel
\begin_inset ERT
status collapsed
@@ -6113,6 +8273,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6135,6 +8306,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
side
\begin_inset ERT
status collapsed
@@ -6146,6 +8328,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6185,6 +8378,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
fnorm
\begin_inset ERT
status collapsed
@@ -6196,6 +8400,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6217,6 +8432,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ftan
\begin_inset ERT
status collapsed
@@ -6228,6 +8454,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6249,6 +8486,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
flux
\begin_inset ERT
status collapsed
@@ -6260,6 +8508,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6278,15 +8537,8 @@
igeom
\series default
unit.
- These constitute the geometry part of the input
-\begin_inset Quotes eld
-\end_inset
-
-deck
-\begin_inset Quotes erd
-\end_inset
-
- for the program
+ These constitute the geometry part of the input ``deck'' for the program
+
\family typewriter
conman
\family default
@@ -6309,6 +8561,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Absolute\InsetSpace ~
Coordinate\InsetSpace ~
Card
@@ -6322,11 +8585,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
node gp (x(i,node) i=1,nsd)
-\emph default
-
\end_layout
\begin_deeper
@@ -6341,6 +8613,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
node
\begin_inset ERT
status collapsed
@@ -6352,6 +8635,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6373,6 +8667,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
gp
\begin_inset ERT
status collapsed
@@ -6384,6 +8689,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6420,6 +8736,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
x(i,node)
\begin_inset ERT
status collapsed
@@ -6431,6 +8758,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6451,6 +8789,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Corner\InsetSpace ~
Generation\InsetSpace ~
Cards
@@ -6464,6 +8813,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
- gp-1 cards
\emph on
node mgen (x(i,node) i=1,nsd)
@@ -6481,6 +8841,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
node
\begin_inset ERT
status collapsed
@@ -6492,6 +8863,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6513,6 +8895,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
mgen
\begin_inset ERT
status collapsed
@@ -6524,6 +8917,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6579,6 +8983,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
x(i,node)
\begin_inset ERT
status collapsed
@@ -6590,6 +9005,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6610,6 +9036,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Generation\InsetSpace ~
Increment\InsetSpace ~
Card
@@ -6623,6 +9060,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
ninc1 inc1 ninc2 inc2
@@ -6640,6 +9088,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ninc1
\begin_inset ERT
status collapsed
@@ -6651,6 +9110,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6672,6 +9142,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
inc1
\begin_inset ERT
status collapsed
@@ -6683,6 +9164,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6704,6 +9196,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ninc2
\begin_inset ERT
status collapsed
@@ -6715,6 +9218,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6742,6 +9256,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
inc2
\begin_inset ERT
status collapsed
@@ -6753,6 +9278,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6791,6 +9327,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Absolute\InsetSpace ~
Velocity\InsetSpace ~
Card
@@ -6804,11 +9351,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
node gp (v(i,node) i=1,nsd)
-\emph default
-
\end_layout
\begin_deeper
@@ -6823,6 +9379,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
node
\begin_inset ERT
status collapsed
@@ -6834,6 +9401,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6855,6 +9433,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
gp
\begin_inset ERT
status collapsed
@@ -6866,6 +9455,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6902,6 +9502,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
v(i,node)
\begin_inset ERT
status collapsed
@@ -6913,6 +9524,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6933,6 +9555,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Corner\InsetSpace ~
Generation\InsetSpace ~
Cards
@@ -6946,11 +9579,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
- gp-1 cards
\emph on
node mgen (v(i,node) i=1,nsd)
-\emph default
-
\end_layout
\begin_deeper
@@ -6965,6 +9607,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
node
\begin_inset ERT
status collapsed
@@ -6976,6 +9629,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -6997,6 +9661,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
mgen
\begin_inset ERT
status collapsed
@@ -7008,6 +9683,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7063,6 +9749,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
v(i,node)
\begin_inset ERT
status collapsed
@@ -7074,6 +9771,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7094,6 +9802,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Generation\InsetSpace ~
Increment\InsetSpace ~
Card
@@ -7107,11 +9826,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
ninc1 inc1 ninc2 inc2
-\emph default
-
\end_layout
\begin_deeper
@@ -7126,6 +9854,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ninc1
\begin_inset ERT
status collapsed
@@ -7137,6 +9876,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7158,6 +9908,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
inc1
\begin_inset ERT
status collapsed
@@ -7169,6 +9930,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7190,6 +9962,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ninc2
\begin_inset ERT
status collapsed
@@ -7201,6 +9984,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7223,6 +10017,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
0
\begin_inset ERT
status collapsed
@@ -7234,6 +10039,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
- if gp equals 2
\end_layout
@@ -7249,6 +10065,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
inc2
\begin_inset ERT
status collapsed
@@ -7260,6 +10087,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7298,6 +10136,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Absolute\InsetSpace ~
Temperature\InsetSpace ~
Card
@@ -7311,11 +10160,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
node gp t(node)
-\emph default
-
\end_layout
\begin_deeper
@@ -7330,6 +10188,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
node
\begin_inset ERT
status collapsed
@@ -7341,6 +10210,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7362,6 +10242,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
gp
\begin_inset ERT
status collapsed
@@ -7373,6 +10264,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7405,6 +10307,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
t(node)
\begin_inset ERT
status collapsed
@@ -7416,6 +10329,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7437,6 +10361,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Corner\InsetSpace ~
Generation\InsetSpace ~
Cards
@@ -7450,11 +10385,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
- gp-1 cards
\emph on
node mgen t(node)
-\emph default
-
\end_layout
\begin_deeper
@@ -7469,6 +10413,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
node
\begin_inset ERT
status collapsed
@@ -7480,6 +10435,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7501,6 +10467,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
mgen
\begin_inset ERT
status collapsed
@@ -7512,6 +10489,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7567,6 +10555,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
t(node)
\begin_inset ERT
status collapsed
@@ -7578,6 +10577,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7599,6 +10609,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Generation\InsetSpace ~
Increment\InsetSpace ~
Card
@@ -7612,11 +10633,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
ninc1 inc1 ninc2 inc2
-\emph default
-
\end_layout
\begin_deeper
@@ -7631,6 +10661,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ninc1
\begin_inset ERT
status collapsed
@@ -7642,6 +10683,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7663,6 +10715,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
inc1
\begin_inset ERT
status collapsed
@@ -7674,6 +10737,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7695,6 +10769,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ninc2
\begin_inset ERT
status collapsed
@@ -7706,6 +10791,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7733,6 +10829,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
inc2
\begin_inset ERT
status collapsed
@@ -7744,6 +10851,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7782,6 +10900,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Absolution\InsetSpace ~
Element\InsetSpace ~
Card
@@ -7795,11 +10924,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
elnu ng mat no (ien(elnu,i) i=1,nen)
-\emph default
-
\end_layout
\begin_deeper
@@ -7814,6 +10952,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
elnu
\begin_inset ERT
status collapsed
@@ -7825,6 +10974,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7846,6 +11006,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ng
\begin_inset ERT
status collapsed
@@ -7857,6 +11028,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7889,6 +11071,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
mat
\begin_inset ERT
status collapsed
@@ -7900,6 +11093,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
no .
.
.
@@ -7920,6 +11124,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
ien(elnu,i)
\begin_inset ERT
status collapsed
@@ -7931,6 +11146,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -7952,6 +11178,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
Increment\InsetSpace ~
Card
\begin_inset ERT
@@ -7964,11 +11201,20 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
\emph on
nel1 incel1 incn1 nel2 incel2 incn2
-\emph default
-
\end_layout
\begin_deeper
@@ -7983,6 +11229,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nel1
\begin_inset ERT
status collapsed
@@ -7994,6 +11251,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -8015,6 +11283,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
incel1
\begin_inset ERT
status collapsed
@@ -8026,6 +11305,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -8047,6 +11337,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
incn1
\begin_inset ERT
status collapsed
@@ -8058,6 +11359,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -8079,6 +11391,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
nel2
\begin_inset ERT
status collapsed
@@ -8090,6 +11413,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -8111,6 +11445,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
incel2
\begin_inset ERT
status collapsed
@@ -8122,6 +11467,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -8143,6 +11499,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
incn2
\begin_inset ERT
status collapsed
@@ -8154,6 +11521,17 @@
\end_inset
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
.
.
.
@@ -8186,33 +11564,79 @@
This is Blankenbach 1a
\end_layout
-\begin_layout LyX-Code
-50 x 50 el.
- plate problem from Blankenbach et al.
- 1989 #Nds sdm dof X Z prc ck echo rrst wrst nus tdvf tseq nelg sky wr 2601
- 2 2 50 50 2 1 0 0 1 102 0 1 1 1 0 time step information 100 1 1.0 1.0 0.50000
- output information 100 100 100 100 velocity boundary condition flags: IFCMT,DEL
-NXTLN bnode enode incr bcf1 bcf2 1 2551 51 0 1 2551 2601 1 1 0 1 51 1 1
- 0 51 2601 51 0 1 1 1 1 1 1 51 51 1 1 1 2551 2551 1 1 1 2601 2601 1 1 1
- 0 0 0 0 0 temperature boundary condition flags 1 2551 51 1 51 2601 51 1
- 0 0 0 0 bndy info (top - bottom rows) 1 2551 51 51 2601 51 0 0 0 bndy info
- (2nd from top - 2nd from bottom rows) 2 2552 51 50 2600 51 0 0 0 initial
- condition information 0.1 1.0 1.0 1.0 element information 2 2500 4 4 1 2 0
- 5 0 0 viscosity 1.0e0 penalty number 0.1E+08 diffusivity (always one) 1.0
- Rayleigh number 1.0e+04 internal heating parameter 0.0 0.0 0.0
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{verbatim}
\end_layout
+\end_inset
+
+ 50 x 50 el.
+ problem for Blankenbach Benchmark numnp nsd ndof nelx nelz prc ck iecho
+ rrst wrst nus tdvf tseq nelg sky wr 2601 2 2 50 50 2 1 0 0 1 102 0 1 1
+ 1 0 time step information 100 1 1.0 1.0 0.50000 output information 100 100
+ 100 100 velocity boundary condition flags bnode enode incr bcf1 bcf2 1
+ 2551 51 0 1 2551 2601 1 1 0 1 51 1 1 0 51 2601 51 0 1 1 1 1 1 1 51 51 1
+ 1 1 2551 2551 1 1 1 2601 2601 1 1 1 0 0 0 0 0 temperature boundary condition
+ flags 1 2551 51 1 51 2601 51 1 0 0 0 0 bndy info (top - bottom rows) 1
+ 2551 51 51 2601 51 0 0 0 bndy info (2nd from top - 2nd from bottom rows)
+ 2 2552 51 50 2600 51 0 0 0 initial condition information 0.1 1.0 1.0 1.0 element
+ information 2 2500 4 4 1 2 0 5 0 0 viscosity 1.0e0 penalty number 0.1E+08
+ diffusivity (always one) 1.0 Rayleigh number 1.0e+04 internal heating parameter
+ 0.0 activation energy 0.0 activation volume 0.0 viscosity cutoff 1.0e7
+\begin_inset ERT
+status collapsed
+
\begin_layout Standard
-The lines below are a sample geometry file for the 50 by 50 element problem.
+
+
+\backslash
+end{verbatim}
\end_layout
-\begin_layout LyX-Code
-coordinates 1 4 0.0 0.0 2551 1 1.0 0.0 2601 1 1.0 1.0 51 1 0.0 1.0 50 51 50 1 0
+\end_inset
+
+ The lines below are a sample geometry file for the 50 by 50 element problem.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{verbatim}
+\end_layout
+
+\end_inset
+
+ coordinates 1 4 0.0 0.0 2551 1 1.0 0.0 2601 1 1.0 1.0 51 1 0.0 1.0 50 51 50 1 0
0 0.0 0.0 velocity boundary conditions (non-zero) 0 0 0.0 0.0 temperature boundary
conditions (non-zero) 1 2 1.0 2551 0 1.0 50 51 0 0 0.0 element connectivity
- and material groups 1 1 1 1 52 53 2 50 50 51 50 1 1 0 0 0 0 0 0 0
+ and material groups 1 1 1 1 52 53 2 50 50 51 50 1 1 0 0 0 0 0 0 0
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{verbatim}
\end_layout
+\end_inset
+
+
+\end_layout
+
\begin_layout Chapter
\begin_inset LatexCommand label
name "cha:Output-Guide"
@@ -8226,6 +11650,1088 @@
The Output Files
\end_layout
+\begin_layout Standard
+The output files names are taken from the names in the runfile.
+ The execution of
+\family typewriter
+conman
+\family default
+ proceeds by % conman.pic < runfile where the runfile has a list of filenames
+ that can be up to 80 characters long.
+\end_layout
+
+\begin_layout Standard
+\noindent
+The names in the runfile are attached to the following input or output files.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{verbatim}
+\end_layout
+
+\end_inset
+
+ input geometry output restart input restart output time series output temperatu
+re (and velocity) field output stress (and viscosity) field output geoid
+ output
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{verbatim}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All files are ASCII files.
+ The
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ input
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
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+\end_layout
+
+\end_inset
+
+ and
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
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+
+\begin_inset ERT
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+
+\end_inset
+
+ geometry
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ files are as described in the previous section.
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
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+
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+\backslash
+em
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+
+\end_inset
+
+ output
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
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+}
+\end_layout
+
+\end_inset
+
+ file is a formatted record of the input.
+ If the variable
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
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+{
+\end_layout
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+
+
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+\begin_inset ERT
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+\begin_layout Standard
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+\end_inset
+
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+ Near the end of the
+\begin_inset ERT
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+{
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+\end_inset
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+\begin_inset ERT
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+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ file execution time is listed for various subparts of the code.
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
+
+{
+\end_layout
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+\end_inset
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+\begin_inset ERT
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+\end_layout
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+\end_inset
+
+ file is an input file that is used if the variable
+\begin_inset ERT
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+
+\begin_inset ERT
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+status collapsed
+
+\begin_layout Standard
+
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+\end_layout
+
+\end_inset
+
+ is set to one.
+ The file is ASCII but formatted and the format statement can be found in
+ the file
+\series bold
+input.F
+\series default
+.
+ The first line contains the initial timestep and time, the second line
+ is a header, and the third through
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
+
+{
+\end_layout
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+\backslash
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+\end_layout
+
+\end_inset
+
+ numnp
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ lines contains the node, temperature and time derivative of temperature.
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
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+
+
+\begin_inset ERT
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+
+\end_inset
+
+ restart output
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ file is an output file that is used if the variable
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
+
+{
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+
+\begin_inset ERT
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+ iorstr
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+\begin_layout Standard
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+\end_layout
+
+\end_inset
+
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+ We recommend this always be set to run.
+ This file is overwritten every
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
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+ nsdprt
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+status collapsed
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+\begin_layout Standard
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+}
+\end_layout
+
+\end_inset
+
+ steps and the output is written from the file
+\series bold
+timdrv.F
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
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+\begin_layout Standard
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+{
+\end_layout
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+\end_inset
+
+
+\begin_inset ERT
+status collapsed
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+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ time series output
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ file is written every time step.
+ The values are ASCII and are heat flux at the bottom, heat flux at the
+ top, kinetic energy, and time.
+ All values are dimensionless.
+ This file is written from the routine
+\series bold
+fluxke.F
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ Temperature and velocity output
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ file is an ASCII file written from the routine
+\series bold
+print.F
+\series default
+.
+ There are two header lines that contain
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
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+
+\backslash
+em
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+
+\end_inset
+
+ nsd, nelx, nelz, numnp, nstep, time
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+ The second line labels the output and the third through numnp lines list
+ the node, x, z, vx, vz, and temperature values at each node.
+ This file is output every
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ nsvprt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ steps and each successive set of values is appended to the end of the file.
+ The unix command
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
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+
+\backslash
+em
+\end_layout
+
+\end_inset
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+ split -
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+numnp+2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ tempfile
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ can be used to split the file into files that are
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ numnp+2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ lines long.
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ Stress output
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ file is an ASCII file written from the routine
+\series bold
+prtstr
+\series default
+ which can be found in the file
+\series bold
+stress.F
+\series default
+.
+ Like the temperature velocity file there are two header lines that contain
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ nsd, nelx, nelz, numnp, nstep, time
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+ The second line labels the output and the third through
+\family typewriter
+numnp
+\family default
+ lines list the node, x, z, txx, tzz.
+ txz.
+ p and viscosity at each node.
+ This file is output every
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ nsvprt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ steps and each successive set of values is appended to the end of the file.
+ The unix command
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ split -
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+numnp+2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ tempfile
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ can be used to split the file into files that are
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ numnp+2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ lines long.
+\end_layout
+
+\begin_layout Standard
+The
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ geoid output
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ file contains the horizontal coordinate, the dynamic topography, the geoid
+ contribution from the temperature only and the total geoid (from surface
+ and cmb topography, and internal (i.e., temperature) density contrasts).
+ This is written from the file
+\series bold
+geoid.F
+\series default
+.
+ The dimensional values are hard wired into the code and can be found at
+ the top of
+\series bold
+geoid.F
+\series default
+.
+ This version of the geoid code has not been tested with flow-through boundary
+ conditions (i.e,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+ nwrap = nelz
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+em
+\end_layout
+
+\end_inset
+
+
+\series bold
+\color red
+Warning.
+
+\series default
+\color inherit
+ As written, the code assumes a Rayleigh number of
+\begin_inset Formula $10^{7}$
+\end_inset
+
+ and does not adjust the parameters as the Rayleigh number changes.
+ This would be a trivial fix but still may not yield the results intended.
+ It is best to carefully check the
+\series bold
+geoid.F
+\series default
+ source for the specific problem if interest.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Chapter
\begin_inset LatexCommand label
name "cha:The-Benchmark-Cases"
@@ -8235,14 +12741,31 @@
The Benchmark Cases
\end_layout
+\begin_layout Standard
+We provide input and geometry files for the benchmark cases described below
+ in the directories
+\family typewriter
+cookbook1
+\family default
+ and
+\family typewriter
+cookbook2
+\family default
+.
+\end_layout
+
\begin_layout Section
-Constant Viscosity Benchmark for ConMan
+Cookbook 1: Constant Viscosity Benchmark for ConMan
\end_layout
\begin_layout Standard
Here we reproduce the results from Blankenbach et al.
- (1989) for constant viscosity in a unit-aspect ratio domain, with free-slip
- boundary conditions, heated from below and cooled from above.
+ (1989)
+\series bold
+[TODO need reference for bibliography]
+\series default
+ for constant viscosity in a unit-aspect ratio domain, with free-slip boundary
+ conditions, heated from below and cooled from above.
The user should note that to run this problem, you will need to modify
the routines
\series bold
@@ -8267,11 +12790,17 @@
\end_inset
respectively and the dimensional parameters are listed in Table\InsetSpace ~
-7.1.
- The time is the run time in seconds for the Picard version of the code
- using 100 iterations on an intel MacPro with two 3\InsetSpace ~
-GHz processors using
- the intel fortran compiler with -O2 optimization.
+
+\begin_inset LatexCommand ref
+reference "tab:Mantle-parameters-for"
+
+\end_inset
+
+.
+ The time is the runtime in seconds for the Picard version of the code using
+ 100 iterations on an intel MacPro with two 3\InsetSpace ~
+GHz processors using the Intel
+ fortran compiler with -O2 optimization.
While the problems in Blankenbach et al.
are specified dimensionally, the equations are solved non-dimensionally
within ConMan for numerical stability and the scaling factors are applied
@@ -8281,25 +12810,43 @@
\begin_layout Standard
The results are computed on uniformly spaced grids and the global properties
of Nusselt number and root-mean-square velocity, as well as the topography
- and geoid at the left and right hand side of the domain are reported, along
- with the extrapolated value from Christensen's results (see Blankenbach
+ and geoid at the left- and right-hand side of the domain are reported,
+ along with the extrapolated value from Christensen's results (see Blankenbach
et al., 1989 for discussion) in Table\InsetSpace ~
-7.2 (Rayleigh number
+
+\begin_inset LatexCommand ref
+reference "tab:Blankenbach-(1989)-Benchmark-1a"
+
+\end_inset
+
+ (Rayleigh number
\begin_inset Formula $10^{4}$
\end_inset
), Table\InsetSpace ~
-7.3 (Rayleigh number
+
+\begin_inset LatexCommand ref
+reference "tab:Blankenbach-(1989)-Benchmark-1b"
+
+\end_inset
+
+ (Rayleigh number
\begin_inset Formula $10^{5}$
\end_inset
), and Table\InsetSpace ~
-7.4 (Rayleigh number
+
+\begin_inset LatexCommand ref
+reference "tab:Blankenbach-(1989)-Benchmark-1c"
+
+\end_inset
+
+ (Rayleigh number
\begin_inset Formula $10^{6}$
\end_inset
).
- For the globally properties of Nusselt number and root-mean-square velocity,
+ For the global properties of Nusselt number and root-mean-square velocity,
the 50 by 50 element grid are within 1% of Christensen's extrapolated results
even for the Rayleigh number
\begin_inset Formula $10^{6}$
@@ -8326,10 +12873,6 @@
status open
\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="4">
@@ -8875,6 +13418,11 @@
\begin_inset Caption
\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Mantle-parameters-for"
+
+\end_inset
+
Mantle parameters for Blankenbach constant viscosity benchmarks.
\end_layout
@@ -9363,11 +13911,7 @@
\end_inset
- Christensen
-\begin_inset Formula $^{\prime}$
-\end_inset
-
-s extrapolated values.
+ Christensen's extrapolated values.
\end_layout
\end_inset
@@ -9447,12 +13991,17 @@
\begin_inset Caption
\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Blankenbach-(1989)-Benchmark-1a"
+
+\end_inset
+
Blankenbach (1989) Benchmark 1a: Steady State, 2D, constant viscosity convection
in a 1 by 1 box with Rayleigh number
\begin_inset Formula $10^{4}$
\end_inset
- using ConMan
+ using ConMan.
\end_layout
\end_inset
@@ -9931,11 +14480,7 @@
\end_inset
- Christensen
-\begin_inset Formula $^{\prime}$
-\end_inset
-
-s extrapolated values.
+ Christensen's extrapolated values.
\end_layout
\end_inset
@@ -10015,12 +14560,17 @@
\begin_inset Caption
\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Blankenbach-(1989)-Benchmark-1b"
+
+\end_inset
+
Blankenbach (1989) Benchmark 1b: Steady State, 2D, constant viscosity convection
in a 1 by 1 box with Rayleigh number
\begin_inset Formula $10^{5}$
\end_inset
- using ConMan
+ using ConMan.
\end_layout
\end_inset
@@ -10499,11 +15049,7 @@
\end_inset
- Christensen
-\begin_inset Formula $^{\prime}$
-\end_inset
-
-s extrapolated values.
+ Christensen's extrapolated values.
\end_layout
\end_inset
@@ -10583,6 +15129,11 @@
\begin_inset Caption
\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Blankenbach-(1989)-Benchmark-1c"
+
+\end_inset
+
Blankenbach (1989) Benchmark 1c: Steady State, 2D, constant viscosity convection
in a 1 by 1 box with Rayleigh number
\begin_inset Formula $10^{6}$
@@ -10602,7 +15153,7 @@
\end_layout
\begin_layout Section
-Temperature-Dependent Viscosity Benchmark for ConMan
+Cookbook 2: Temperature-Dependent Viscosity Benchmark for ConMan
\end_layout
\begin_layout Standard
@@ -10616,7 +15167,7 @@
\end_inset
- where
+where
\begin_inset Formula $\eta_{o}=2.9\times10^{19}$
\end_inset
@@ -10626,13 +15177,25 @@
.
The other scaling parameters are the same as Table\InsetSpace ~
-7.1.
+
+\begin_inset LatexCommand ref
+reference "tab:Mantle-parameters-for"
+
+\end_inset
+
+.
The results for a Rayleigh number of
\begin_inset Formula $10^{4}$
\end_inset
are presented in Table\InsetSpace ~
-7.5.
+
+\begin_inset LatexCommand ref
+reference "tab:Blankenbach-(1989)-Benchmark-2a"
+
+\end_inset
+
+.
Here once again the global properties of Nusselt number and root-mean-square
velocity for the 50 by 50 grid are within 1-2% of Christensen's extrapolated
results; however, in contrast to the constant viscosity cases, the values
@@ -11182,11 +15745,7 @@
\end_inset
- Christensen
-\begin_inset Formula $^{\prime}$
-\end_inset
-
-s extrapolated values.
+ Christensen's extrapolated values.
\end_layout
\end_inset
@@ -11266,6 +15825,11 @@
\begin_inset Caption
\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Blankenbach-(1989)-Benchmark-2a"
+
+\end_inset
+
Blankenbach (1989) Benchmark 2a: Steady State, 2D, temperature-dependent
viscosity convection (b=6.907755279) in a 1 by 1 box with Rayleigh number
@@ -11285,7 +15849,90 @@
\end_layout
+\begin_layout Section
+Cookbook 3: Constant Viscosity Driven Slab Problem for ConMan
+\end_layout
+
\begin_layout Standard
+This geometry is based on the subduction zone benchmark by
+\begin_inset LatexCommand cite
+key "van Keken et al 2008"
+
+\end_inset
+
+.
+ A thermal structure from this is presented on the cover.
+ The purpose here is to illustrate how one can (with some struggle) implement
+ a deformed and variable mesh with the fairly basic grid generator in ConMan.
+ One can use a more advanced grid generator and input the coordinates of
+ every node directly as well as the
+\series bold
+ien
+\series default
+ array for each element.
+\end_layout
+
+\begin_layout Standard
+This problem will not reproduce the exact result presented in
+\begin_inset LatexCommand cite
+key "van Keken et al 2008"
+
+\end_inset
+
+ because this version of ConMan does not have the discontinuous velocity
+ field, which turns out to be critical to match the benchmark results.
+ The resulting thermal structure should look like Figure\InsetSpace ~
+
+\begin_inset LatexCommand ref
+reference "fig:wedge"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:wedge"
+
+\end_inset
+
+ Thermal structure for the wedge problem in Cookbook 3 example.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+ filename images/wedge.pdf
+ scale 60
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
\start_of_appendix
\begin_inset ERT
status collapsed
@@ -11303,8 +15950,24 @@
\end_inset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+%dummy comment inserted by tex2lyx to ensure that this paragraph is not
+ empty
\end_layout
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Chapter
License
\end_layout
@@ -11443,6 +16106,7 @@
Program is covered only if its contents constitute a work based on the
Program (independent of having been made by running the Program).
Whether that is true depends on what the Program does.
+
\end_layout
\begin_layout Enumerate
@@ -11727,6 +16391,7 @@
YOU.
SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY
SERVICING, REPAIR OR CORRECTION.
+
\end_layout
\begin_layout Itemize
@@ -11760,6 +16425,7 @@
THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY
OF SUCH DAMAGES.
+
\end_layout
\begin_layout Section*
@@ -11873,30 +16539,34 @@
\end_inset
-Brooks, A., 1981.
- A Petrov-Galerkin finite-element formulation for convection dominated flows.
- Ph.D.
- Thesis, California Institute of Technology, Pasadena, CA.
+Brooks, A.N.
+
+\emph on
+A Petrov-Galerkin finite-element formulation for convection dominated flows.
+
+\emph default
+ Unpublished doctoral thesis, California Institute of Technology, Pasadena,
+ CA, 1981.
\end_layout
\begin_layout Bibliography
\begin_inset LatexCommand bibitem
label "2"
-key "Brooks and Hughes"
+key "Brooks and Hughes 1990"
\end_inset
Brooks, A.N.
- and Hughes, T.J.R., 1982.
- Streamline upwind/Petrov-Galerkin formulatins for convection dominated
- flows with particular emphasis on the inpompressible Navier-Stokes equations.
+ and Hughes, T.J.R.
+ (1990), Streamline upwind/Petrov-Galerkin formulations for convection dominated
+ flows with particular emphasis on the incompressible Navier-Stokes equations.
\emph on
Comp.
Meth.
in Appl.
Mech.
- and Eng., 32,
+ and Eng., 81(3),
\emph default
199-259.
\end_layout
@@ -11908,31 +16578,35 @@
\end_inset
-Hughes, T.J.R., 1987.
+Hughes, T.J.R.
\emph on
The finite element method.
\emph default
- Prentice-Hall, Inc., Englewood Cliffs, New Jersey
+ Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1987.
\end_layout
\begin_layout Bibliography
\begin_inset LatexCommand bibitem
label "4"
-key "Hughes and Brooks 1987"
+key "Hughes and Brooks 1979"
\end_inset
Hughes, T.J.R.
- and Brookes, A.N., 1987.
- A multi-dimensional upwind scheme with no crosswind diffusion.
- In: Finite element methods for convection dominated flows.
+ and Brooks, A.N.
+ (1979), A multi-dimensional upwind scheme with no crosswind diffusion.
+ In: Finite element methods for convection dominated flows (T.J.R.
+ Hughes, ed.),
+\emph on
+ASME,
+\emph default
\emph on
-ASME
+34
\emph default
-, New York, 34:19-35.
+, 19-35.
\end_layout
\begin_layout Bibliography
@@ -11942,15 +16616,22 @@
\end_inset
-Hughes, T.J.R., Franca, L.P., Hulbert, G.M., Johan, Z., and Shakib, F., 1988.
- The Galerkin/least-squares method for advective-diffusive equations.
- In: Recent developments in computational fluid dynamics.
- T.E.
- Tezduyar (Editor),
+Hughes, T.J.R., Franca, L.P., Hulbert, G.M., Johan, Z., and Shakib, F.
+ (1988), The Galerkin/least-squares method for advective-diffusive equations,
+ in
\emph on
+Recent developments in computational fluid dynamics
+\emph default
+ (T.E.
+ Tezduyar, ed.),
+\emph on
ASME,
\emph default
- New York, 95:75-99.
+
+\emph on
+95
+\emph default
+, 75-99.
\end_layout
\begin_layout Bibliography
@@ -11960,16 +16641,20 @@
\end_inset
-Hughes, T.J.R., Liu, W.K., and Brooks, A.N., 1979.
- Finite element analysis of incompressible viscous flows by the penalty
- function formulation.
+Hughes, T.J.R., Liu, W.K., and Brooks, A.N.
+ (1979), Finite element analysis of incompressible viscous flows by the
+ penalty function formulation.
\emph on
J.
Comput.
Phys.,
\emph default
- 30: 19-35.
+
+\emph on
+30
+\emph default
+, 1-60.
\end_layout
\begin_layout Bibliography
@@ -11980,9 +16665,9 @@
\end_inset
Malkus, D.S.
- and Hughes, T.J.R., 1978.
- Mixed finite element methods reduced and selective integration techniques:
- a unification of concepts.
+ and Hughes, T.J.R.
+ (1978), Mixed finite element methods reduced and selective integration
+ techniques: a unification of concepts.
\emph on
Comp.
@@ -11991,7 +16676,11 @@
Mech.
and Eng.,
\emph default
- 15, 63-81.
+
+\emph on
+15
+\emph default
+, 63-81.
\end_layout
\begin_layout Bibliography
@@ -12001,61 +16690,56 @@
\end_inset
-Temam, R., 1977.
- Navier-Stokes equations: therory and numerical analysis.
+Temam, R.
+
+\emph on
+Navier-Stokes equations: theory and numerical analysis
+\emph default
+.
North-Holland.
- Amsterdam.
+ Amsterdam, 1977.
\end_layout
\begin_layout Bibliography
\begin_inset LatexCommand bibitem
label "9"
-key "Travis et al 1991"
+key "Travis et al 1990"
\end_inset
-Travis, B.J., C.
- Anderson, J.
- Baumgardner, C.
- Gable, B.H.
- Hager, P.
- Olson, R.J.
- O
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-
-\backslash
-textquoteright
+Travis, B.J., Anderson, C., Baumgardner, J., Gable, C.W., Hager, B.H., O'Connell,
+ R.J., Olson, P., Raefsky, A.
+ and Schubert, G.
+ (1990), A benchmark comparison of numerical methods for infinite Prandtl
+ number convection in two-dimensional Cartesian geometry,
+\emph on
+Geophys.
+ Astrophys.
+ Fluid Dynamics,
+\emph default
+
+\emph on
+55
+\emph default
+, 137-160, doi: 10.1080/03091929008204111
\end_layout
-\end_inset
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+label "9"
+key "van Keken et al 2008"
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-{}
-\end_layout
-
\end_inset
-Connell, A.
- Raefsky, and G.
- Schubert, 1991.
- A benchmark comparison of numerical methods for infinite Prandtl number
- convection in two-dimensional Cartesian geometry,
+ van Keken, P.E., Currie, C., King, S.D., Behn, M.D., Canioncle, A., He, J., Katz,
+ R.F., Lin, S.-C., Parmentier, E.M., Spiegelman, M., and Wang, K.
+ (2008), A community benchmark for subduction zone modeling,
\emph on
-Geophys.
- Astrophys.
- Fluid Dynamics,
+Phys.
+ Earth Planet.
+ Int.
\emph default
- in press.
-
+, in press.
\end_layout
\end_body
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