[cig-commits] r7920 - doc/CitcomS/manual
tan2 at geodynamics.org
tan2 at geodynamics.org
Fri Aug 31 13:53:30 PDT 2007
Author: tan2
Date: 2007-08-31 13:53:29 -0700 (Fri, 31 Aug 2007)
New Revision: 7920
Modified:
doc/CitcomS/manual/citcoms.lyx
Log:
Update the manual up to section 1.6
Modified: doc/CitcomS/manual/citcoms.lyx
===================================================================
--- doc/CitcomS/manual/citcoms.lyx 2007-08-30 20:55:49 UTC (rev 7919)
+++ doc/CitcomS/manual/citcoms.lyx 2007-08-31 20:53:29 UTC (rev 7920)
@@ -1,4 +1,4 @@
-#LyX 1.4.3 created this file. For more info see http://www.lyx.org/
+#LyX 1.4.2 created this file. For more info see http://www.lyx.org/
\lyxformat 245
\begin_document
\begin_header
@@ -91,7 +91,7 @@
\begin_layout Author
© California Institute of Technology
\newline
-Version 2.2.1
+Version 3.0.0
\end_layout
\begin_layout Date
@@ -579,8 +579,8 @@
\end_layout
\begin_layout Standard
-This release of CitComS (2.2) incorporates the ability of tracing particles
- in the flow.
+The fourth major release of CitComS (2.2) incorporates the ability of tracing
+ particles in the flow.
The tracer code was developed by Allen McNamara and Shijie Zhong in 2004
and donated to CIG in early 2007.
The tracer code has a wide range of applications in the mantle convection.
@@ -589,6 +589,15 @@
or in tracking the evolution of the chemical composition field.
\end_layout
+\begin_layout Standard
+This release of CitComS (3.0) contains several new features: 1) two implementatio
+ns of compressible convection, one by Wei Leng and Shijie Zhong and the
+ other by Eh Tan; 2) the ability to resume computation from previous checkpoints
+; 3) multi-component chemical convection; 4) compressed ASCII output by
+ Thorsten Becker; 5) reading in initial temperature and tracer location
+ from GRD files by Thorsten Becker; 6)solver coupling.
+\end_layout
+
\begin_layout Section
About Pyre
\end_layout
@@ -725,16 +734,16 @@
\end_layout
\begin_layout Standard
-With CitComS, the mantle is treated as an incompressible viscous spherical
- shell.
- With these assumptions, thermal convection is governed by the equations
- for conservation of mass, momentum, and energy:
+With CitComS, the mantle is treated as an anelastic, compressible, viscous
+ spherical shell under Truncated Anelastic Liquid Approximation.
+ With these assumptions, thermal convection is governed by the non-dimensionaliz
+ed equations for conservation of mass, momentum, and energy:
\end_layout
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-u_{i,i}=0\label{eq:conservation of mass}\end{equation}
+\left(\rho u_{i}\right)_{,i}=0\label{eq:conservation of mass}\end{equation}
\end_inset
@@ -744,7 +753,7 @@
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
--P_{,i}+(\eta u_{i,j}+\eta u_{j,i})_{,j}+\delta\rho g\delta_{ir}=0\label{eq:conservation of momentum}\end{equation}
+-P_{,i}+\left(\eta(u_{i,j}+u_{j,i}-\frac{2}{3}u_{k,k}\delta_{ij})\right)_{,i}+\delta\rho g\delta_{ir}=0\label{eq:conservation of momentum}\end{equation}
\end_inset
@@ -754,7 +763,7 @@
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-T_{,t}+u_{i}T_{,i}=\kappa T_{,ii}+H\label{eq:conservation of energy}\end{equation}
+\rho C_{P}\left(T_{,t}+u_{i}T_{,i}\right)=\rho C_{P}\kappa T_{,ii}+latent+\rho\alpha gu_{r}\left(T+T_{0}\right)+\Phi+\rho H\label{eq:conservation of energy}\end{equation}
\end_inset
@@ -765,13 +774,29 @@
\noindent
where
\emph on
-u
+
+\begin_inset Formula $\rho$
+\end_inset
+
+
+\shape italic
+ is the density,
+\shape default
+ u
\emph default
is the velocity,
\emph on
P
\emph default
is the dynamic pressure,
+\begin_inset Formula $\eta$
+\end_inset
+
+ is the viscosity,
+\begin_inset Formula $\delta_{ij}$
+\end_inset
+
+ is the Kroneker delta tensor,
\begin_inset Formula $\delta\rho$
\end_inset
@@ -780,18 +805,34 @@
g
\emph default
is the gravitational acceleration,
-\begin_inset Formula $\eta$
-\end_inset
-
- is the viscosity,
\emph on
T
\emph default
is the temperature,
+\begin_inset Formula $T_{0}$
+\end_inset
+
+ is the temperature at the surface,
+\begin_inset Formula $C_{P}$
+\end_inset
+
+ is the heat capacity,
+\shape italic
+
+\shape default
+
\begin_inset Formula $\kappa$
\end_inset
- is the thermal diffusivity, and
+ is the thermal diffusivity,
+\begin_inset Formula $\alpha$
+\end_inset
+
+ is the thermal expansivity,
+\begin_inset Formula $\Phi$
+\end_inset
+
+ is the viscous dissipation (TODO: unfinised) and
\emph on
H
\emph default
@@ -825,21 +866,103 @@
\end_inset
is time.
- Without phase transitions and composition variation, the density anomalies
- are:
+ With phase transitions and temperature and composition variation, the density
+ anomalies are:
\end_layout
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-\delta\rho=-\alpha\rho_{0}(T-T_{0})\label{eq:density anomalies}\end{equation}
+\delta\rho=-\alpha\bar{\rho}(T-\bar{T_{a}})+\delta\rho_{ph}\Gamma+\delta\rho_{ch}C\label{eq:density anomalies}\end{equation}
\end_inset
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+where
+\emph on
+
+\begin_inset Formula $\bar{\rho}$
+\end_inset
+
+
+\shape italic
+ is the radial profile of density,
+\shape default
+\emph default
+
+\begin_inset Formula $\bar{T_{a}}$
+\end_inset
+
+ is the radial profile
+\emph on
+
+\emph default
+of adiabatic temperature,
+\emph on
+
+\emph default
+
+\begin_inset Formula $\delta\rho_{ph}$
+\end_inset
+
+ is the density jump across a phase change, and
+\begin_inset Formula $\delta\rho_{ch}$
+\end_inset
+
+ is the density difference between the compositions
+\emph on
+,
+\begin_inset Formula $\Gamma$
+\end_inset
+
+
+\shape italic
+is the phase function, and
+\shape default
+C
+\emph default
+ is the composition.
+ The phase functin is defined as:
\end_layout
\begin_layout Standard
+\align right
+\begin_inset Formula \begin{equation}
+\Gamma=\frac{1}{2}\left(1+\tanh\left(\frac{1-r-d_{ph}-s(T-T_{ph})}{w_{ph}}\right)\right)\label{eq:17}\end{equation}
+
+\end_inset
+
+ (TODO: Sue, can you fix the eqn #?)
+\end_layout
+
+\begin_layout Standard
+\noindent
+where
+\begin_inset Formula $d_{ph}$
+\end_inset
+
+ and
+\begin_inset Formula $T_{ph}$
+\end_inset
+
+ are the ambient depth and temperature of a phase change,
+\emph on
+ s
+\emph default
+ is the Clapeyron slope of a phase change, and
+\begin_inset Formula $w_{ph}$
+\end_inset
+
+ is the width of a phase transition.
+
+\end_layout
+
+\begin_layout Standard
These equations lead to the following normalization in which primed quantities
are nondimensional:
\end_layout
@@ -886,7 +1009,7 @@
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-\gamma=\frac{HR_{0}^{2}}{\kappa\Delta T}\label{eq:9}\end{equation}
+H=C_{P0}\Delta TH^{'}\label{eq:9}\end{equation}
\end_inset
@@ -919,7 +1042,7 @@
\begin_inset Formula $\rho_{0}$
\end_inset
-is the reference density,
+ is the reference density,
\begin_inset Formula $R_{0}$
\end_inset
@@ -927,7 +1050,11 @@
\begin_inset Formula $\eta_{0}$
\end_inset
- is a reference viscosity, and
+ is a reference viscosity,
+\begin_inset Formula $C_{P0}$
+\end_inset
+
+ is the reference heat capacity, and
\begin_inset Formula $\Delta T$
\end_inset
@@ -938,7 +1065,7 @@
\begin_layout Standard
\begin_inset Formula \begin{equation}
-u_{i,i}=0\label{eq:12}\end{equation}
+u_{i,i}+\frac{d\ln\bar{\rho}}{dr}u_{r}=0\label{eq:12}\end{equation}
\end_inset
@@ -947,7 +1074,7 @@
\begin_layout Standard
\begin_inset Formula \begin{equation}
--P_{,i}+(\eta u_{i,j}+\eta u_{j,i})_{,j}+RaT\delta_{ir}=0\label{eq:13}\end{equation}
+-P_{,i}+\left(\eta(u_{i,j}+u_{j,i}-\frac{2}{3}u_{k,k}\delta_{ij})\right)_{,i}+(RaT+Rab\Gamma-RacC)\delta_{ir}=0\label{eq:13}\end{equation}
\end_inset
@@ -957,7 +1084,7 @@
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-T_{,t}+u_{i}T_{,i}=T_{,ii}+\gamma\label{eq:14}\end{equation}
+T_{,t}+u_{i}T_{,i}=T_{,ii}+H+(TODO)\label{eq:14}\end{equation}
\end_inset
@@ -999,60 +1126,6 @@
\end_inset
are about a factor of 8 larger than by the usual definition.
-\end_layout
-
-\begin_layout Standard
-If there is a phase change, equation
-\begin_inset LatexCommand \ref{eq:13}
-
-\end_inset
-
- is modified to:
-\end_layout
-
-\begin_layout Standard
-\align right
-\begin_inset Formula \begin{equation}
--P_{,i}+(\eta u_{i,j}+\eta u_{j,i})_{,j}+(RaT+Rab\Gamma-RacC)\delta_{ir}=0\label{eq:16}\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align right
-\begin_inset Formula \begin{equation}
-\Gamma=\frac{1}{2}\left(1+\tanh\left(\frac{1-r-d_{ph}-s(T-T_{ph})}{w_{ph}}\right)\right)\label{eq:17}\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-where
-\emph on
-C
-\emph default
- is the composition,
-\begin_inset Formula $d_{ph}$
-\end_inset
-
- and
-\begin_inset Formula $T_{ph}$
-\end_inset
-
- are the ambient depth and temperature of a phase change,
-\emph on
- s
-\emph default
- is the Clapeyron slope of a phase change, and
-\begin_inset Formula $w_{ph}$
-\end_inset
-
- is the width of a phase transition.
The phase-change Rayleigh number,
\begin_inset Formula $Rab$
\end_inset
@@ -1084,19 +1157,6 @@
\end_layout
-\begin_layout Standard
-\noindent
-where
-\begin_inset Formula $\delta\rho_{ph}$
-\end_inset
-
- is the density jump across a phase change, and
-\begin_inset Formula $\delta\rho_{ch}$
-\end_inset
-
- is the density difference between the compositions.
-\end_layout
-
\begin_layout Section
Numerical Methods
\end_layout
@@ -1152,7 +1212,7 @@
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-\mathrm{\mathbf{B}^{\mathit{T}}\mathit{u=0}}\label{eq:19}\end{equation}
+\mathrm{\left(\mathbf{B}^{\mathit{T}}+\mathbf{C}\right)\mathit{u=0}}\label{eq:19}\end{equation}
\end_inset
@@ -1179,11 +1239,20 @@
\emph on
u
\emph default
- is a vector of unknown velocities;
+ is a vector of unknown velocities,
\begin_inset Formula $\mathbf{B}$
\end_inset
is the discrete gradient operator,
+\begin_inset Formula $\mathbf{C}$
+\end_inset
+
+ is the second term in equation
+\begin_inset LatexCommand \ref{eq:12}
+
+\end_inset
+
+,
\emph on
p
\emph default
@@ -1200,7 +1269,11 @@
\begin_inset Formula $\mathbf{B}$
\end_inset
-, and
+,
+\begin_inset Formula $\mathbf{C}$
+\end_inset
+
+ and
\emph on
f
\emph default
@@ -1216,7 +1289,7 @@
\end_inset
can be transformed by premultiplying by
-\begin_inset Formula $\mathrm{\mathbf{B}^{\mathit{T}}\mathit{\mathbf{A}^{\mathbf{\mathit{-1}}}}}$
+\begin_inset Formula $\mathrm{\left(\mathbf{B}^{\mathit{T}}+\mathbf{C}\right)\mathit{\mathbf{A}^{\mathbf{\mathit{-1}}}}}$
\end_inset
and using equation
@@ -1230,7 +1303,7 @@
\begin_layout Standard
\align right
\begin_inset Formula \begin{equation}
-\mathbf{B}^{\mathit{T}}\mathit{\mathbf{A}^{\mathbf{\mathit{-1}}}\mathbf{B}\mathit{p=\mathbf{B^{\mathit{T}}A^{\mathit{-1}}\mathit{f}}}}\label{eq:21}\end{equation}
+\left(\mathbf{B}^{\mathit{T}}+\mathbf{C}\right)\mathit{\mathbf{A}^{\mathbf{\mathit{-1}}}\mathbf{B}\mathit{p=\mathbf{\left(\mathbf{B}^{\mathit{T}}+\mathbf{C}\right)A^{\mathit{-1}}\mathit{f}}}}\label{eq:21}\end{equation}
\end_inset
@@ -1245,12 +1318,13 @@
\end_inset
, which simultaneously yields the velocity field.
- A conjugate gradient scheme for this iteration is described by
+ A conjugate gradient scheme
\begin_inset LatexCommand \cite{Ramage/Wathen Iterative solution,Atanga/Silvester Iterative methods}
\end_inset
-, and forms the basis for the technique used in CitComS.
+ or a bi-conjugate gradient stablized scheme is used for this iteration
+ and forms the basis for the technique used in CitComS.
\end_layout
\begin_layout Section
@@ -1761,7 +1835,7 @@
\end_layout
\begin_layout LyX-Code
-$ tar xzf CitcomS-2.2.1.tar.gz
+$ tar xzf CitcomS-3.0.0.tar.gz
\end_layout
\begin_layout Standard
@@ -1769,7 +1843,7 @@
\end_layout
\begin_layout LyX-Code
-$ gunzip -c CitcomS-2.2.1.tar.gz | tar xf -
+$ gunzip -c CitcomS-3.0.0.tar.gz | tar xf -
\end_layout
\begin_layout Section
@@ -1791,7 +1865,7 @@
\newline
\newline
-$ cd CitcomS-2.2.1
+$ cd CitcomS-3.0.0
\end_layout
\begin_layout Enumerate
@@ -1934,7 +2008,7 @@
\end_layout
\begin_layout LyX-Code
-$ cd CitcomS-2.2.1
+$ cd CitcomS-3.0.0
\end_layout
\begin_layout LyX-Code
@@ -2923,7 +2997,7 @@
\end_inset
.
- The CitComS v2.2.1 source package was created with Autoconf 2.59, Automake
+ The CitComS v3.0.0 source package was created with Autoconf 2.59, Automake
1.9.2, and Libtool 1.5.6.
\end_layout
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