[cig-commits] commit: Update manual
Mercurial
hg at geodynamics.org
Mon May 16 21:03:27 PDT 2011
changeset: 353:517083c9295a
user: Walter Landry <wlandry at caltech.edu>
date: Mon May 16 20:55:31 2011 -0700
files: doc/gale.lyx
description:
Update manual
diff -r 90759de8302f -r 517083c9295a doc/gale.lyx
--- a/doc/gale.lyx Mon May 16 20:54:54 2011 -0700
+++ b/doc/gale.lyx Mon May 16 20:55:31 2011 -0700
@@ -106,7 +106,7 @@ Walter Landry and Luke Hodkinson
\begin_inset Newline newline
\end_inset
-Version 1.6.1
+Version 1.6.2
\end_layout
\begin_layout Date
@@ -1870,7 +1870,7 @@ geodynamics.org/cig/software/packages/lo
.
Then you can run Gale from the command line or DOS prompt.
CIG provides binaries for Linux, Mac OS X (10.4 or greater), and Windows
- (2000 and XP).
+ (Vista and 7).
\end_layout
\begin_layout Section
@@ -1888,24 +1888,31 @@ System Requirements
\begin_layout Standard
Gale works on a variety of computational platforms and has been tested on
- workstations running
+ machines running
\end_layout
\begin_layout Itemize
-Mac OS X 10.4.6 (Intel)
+Mac OS X 10.4.6 and 10.6.0
\end_layout
\begin_layout Itemize
-Windows Vista
+Windows Vista (32 and 64 bit)
\end_layout
\begin_layout Itemize
-Debian stable (x86 and AMD64), testing (x86 and AMD64), and unstable (x86)
-\end_layout
-
-\begin_layout Standard
-Gale has also been tested on clusters running RedHat Enterprise Linux 3
- (EM64T).
+Debian stable (AMD64)
+\end_layout
+
+\begin_layout Itemize
+Ubuntu Hardy Heron (x86 and AMD64)
+\end_layout
+
+\begin_layout Itemize
+RedHat Enterprise Linux 3 (EM64T)
+\end_layout
+
+\begin_layout Itemize
+Rocks 4.1 (Opteron)
\end_layout
\begin_layout Subsection
@@ -1913,8 +1920,8 @@ Dependencies
\end_layout
\begin_layout Standard
-In order to build Gale, you must have the headers and development libraries
- for
+In order to build Gale, you must have a C++ compiler and the headers and
+ development libraries for
\end_layout
\begin_layout Itemize
@@ -1937,6 +1944,10 @@ You must also have python 2.2.1 or great
PETSc can install for you.
\end_layout
+\begin_layout Standard
+For checkpointing, you will also need HDF5.
+\end_layout
+
\begin_layout Subsection
\begin_inset CommandInset label
LatexCommand label
@@ -2220,7 +2231,7 @@ If you downloaded binaries for your plat
\end_layout
\begin_layout LyX-Code
-./Gale-1_6_1 input/cookbook/yielding.xml
+./Gale-1_6_2 input/cookbook/yielding.xml
\end_layout
\begin_layout Standard
@@ -2290,7 +2301,7 @@ Due to quirks in some implementations of
Due to quirks in some implementations of MPI, you may have to specify the
complete path to the input file (e.g.,
\family typewriter
-./Gale-1_6_1 /home/juser/gale/input/cookbook/yielding.xml
+./Gale-1_6_2 /home/juser/gale/input/cookbook/yielding.xml
\family default
).
\end_layout
@@ -2570,7 +2581,7 @@ One solution is to use a direct solver i
\end_layout
\begin_layout LyX-Code
-./Gale-1_6_1 input/cookbook/yielding.xml -pc_type lu -ksp_type preonly
+./Gale-1_6_2 input/cookbook/yielding.xml -pc_type lu -ksp_type preonly
\end_layout
\begin_layout Standard
@@ -2599,7 +2610,7 @@ Once that is done, enabling it is again
\end_layout
\begin_layout LyX-Code
-./Gale-1_6_1 input/cookbook/yielding.xml -pc_factor_mat_solver_package mumps
+./Gale-1_6_2 input/cookbook/yielding.xml -pc_factor_mat_solver_package mumps
\backslash
@@ -2746,7 +2757,7 @@ You can also change the default values o
\end_layout
\begin_layout LyX-Code
-./Gale-1_6_1 input/cookbook/yielding.xml --maxTimeSteps=20
+./Gale-1_6_2 input/cookbook/yielding.xml --maxTimeSteps=20
\end_layout
\begin_layout Standard
@@ -2757,7 +2768,7 @@ You can append any number of modified pa
\begin_layout LyX-Code
\size small
-./Gale-1_6_1 input/cookbook/yielding.xml --maxTimeSteps=20 --dim=3 --elementResI=
+./Gale-1_6_2 input/cookbook/yielding.xml --maxTimeSteps=20 --dim=3 --elementResI=
64
\begin_inset Newline newline
\end_inset
@@ -4670,7 +4681,7 @@ Modify the bottom boundary condition of
\end_layout
\begin_layout LyX-Code
- <param name="value">StepFunction</param>
+ <param name="value">Equation1</param>
\end_layout
\begin_layout LyX-Code
@@ -4686,35 +4697,19 @@ Modify the bottom boundary condition of
\end_layout
\begin_layout Standard
-This makes the velocity of the bottom boundary a step function.
-
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-You must also specify the parameters of the step function by adding the
- variables
-\end_layout
-
-\begin_deeper
-\begin_layout LyX-Code
-<param name="StepFunctionLowerOffset">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionUpperOffset">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionValue">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionDim">0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionLessThan">False</param>
+This lets you set the x-velocity of the bottom boundary to an arbitrary
+ equation.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Specify the x-velocity equation by adding the variable
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="Equation1">step(0.5-x)</param>
\end_layout
\begin_layout Standard
@@ -5062,11 +5057,7 @@ wrapTop
\end_deeper
\begin_layout Enumerate
-Now specify the velocity on the boundaries using the
-\family typewriter
-StepFunctionProduct
-\family default
- functions.
+Now specify the velocity on the boundaries.
For the left boundary, modify the left
\family typewriter
WallVC
@@ -5100,7 +5091,7 @@ WallVC
\end_layout
\begin_layout LyX-Code
- <param name="value">StepFunctionProduct3</param>
+ <param name="value">Equation1</param>
\end_layout
\begin_layout LyX-Code
@@ -5120,15 +5111,7 @@ and add the variables at the end of the
\end_layout
\begin_layout LyX-Code
-<param name="StepFunctionProduct3Start">0.1</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct3End">0.2</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct3Value">1</param>
+<param name="Equation1">step(y-0.1)*step(0.2-y)</param>
\end_layout
\end_deeper
@@ -5166,7 +5149,7 @@ WallVC
\end_layout
\begin_layout LyX-Code
- <param name="value">StepFunctionProduct2</param>
+ <param name="value">Equation2</param>
\end_layout
\begin_layout LyX-Code
@@ -5186,7 +5169,7 @@ WallVC
\end_layout
\begin_layout LyX-Code
- <param name="value">StepFunctionProduct1</param>
+ <param name="value">Equation3</param>
\end_layout
\begin_layout LyX-Code
@@ -5206,27 +5189,11 @@ and add the variables to the end of the
\end_layout
\begin_layout LyX-Code
-<param name="StepFunctionProduct1Start">0.9</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct1End">1.1</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct1Value">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct2Start">0.9</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct2End">1.1</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="StepFunctionProduct2Value">-1.0</param>
+<param name="Equation2">-step(x-0.9)*step(1.1-x)</param>
+\end_layout
+
+\begin_layout LyX-Code
+<param name="Equation3">step(x-0.9)*step(1.1-x)</param>
\end_layout
\end_deeper
@@ -6103,10 +6070,6 @@ Geometry and boundary conditions for the
\end_layout
-\begin_layout Plain Layout
-
-\end_layout
-
\end_inset
@@ -6177,314 +6140,49 @@ SurfaceAdaptor
\end_deeper
\begin_layout Enumerate
-Replace the left boundary condition for the velocity
-\end_layout
-
-\begin_deeper
-\begin_layout LyX-Code
-<struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">WallVC</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="wall">left</param>
-\end_layout
-
-\begin_layout LyX-Code
- <list name="variables">
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vx</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">StepFunctionProduct3</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- </list>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\begin_layout Standard
-with
-\end_layout
-
-\begin_layout LyX-Code
-<struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">WallVC</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="wall">left</param>
-\end_layout
-
-\begin_layout LyX-Code
- <list name="variables">
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vx</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">Velocity_PartialRotationX</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vy</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">Velocity_PartialRotationY</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- </list>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Replace the bottom boundary condition
-\end_layout
-
-\begin_deeper
-\begin_layout LyX-Code
-<struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">WallVC</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="wall">bottom</param>
-\end_layout
-
-\begin_layout LyX-Code
- <list name="variables">
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vy</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">StepFunctionProduct2</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vx</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">StepFunctionProduct1</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- </list>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\begin_layout Standard
-with
-\end_layout
-
-\begin_layout LyX-Code
-<struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">WallVC</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="wall">bottom</param>
-\end_layout
-
-\begin_layout LyX-Code
- <list name="variables">
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vx</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">Velocity_PartialRotationX</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- <struct>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="name">vy</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="type">func</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="value">Velocity_PartialRotationY</param>
-\end_layout
-
-\begin_layout LyX-Code
- </struct>
-\end_layout
-
-\begin_layout LyX-Code
- </list>
-\end_layout
-
-\begin_layout LyX-Code
-</struct>
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Finally, replace the
-\family typewriter
-StepFunction
-\family default
- variables
-\end_layout
-
-\begin_deeper
-\begin_layout LyX-Code
- <param name="StepFunctionProduct3Start">0.1</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct3End">0.2</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct3Value">1</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct1Start">0.9</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct1End">1.1</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct1Value">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct2Start">0.9</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct2End">1.1</param>
-\end_layout
-
-\begin_layout LyX-Code
- <param name="StepFunctionProduct2Value">-1.0</param>
-\end_layout
-
-\begin_layout Standard
-with rotation variables
-\end_layout
-
-\begin_layout LyX-Code
- <param name="SolidBodyRotationOmega">-1</param>
-\end_layout
-
+Replace the
+\family typewriter
+Equation
+\family default
+ strings
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+ <param name="Equation1">step(y-0.1)*step(0.2-y)</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Equation2">-step(x-0.9)*step(1.1-x)</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Equation3">step(x-0.9)*step(1.1-x)</param>
+\end_layout
+
+\begin_layout Standard
+with
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Equation1">r=hypot(x,y+3); step(r-3.15)*step(3.35-r)*(y+3)/r</param
+>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Equation2">r=hypot(x,y+3); step(r-3.15)*step(3.35-r)*x/r</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Equation3">Equation1</param>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Add parameters for the bottom surface shape
+\end_layout
+
+\begin_deeper
\begin_layout LyX-Code
<param name="SolidBodyRotationCentreX">0</param>
\end_layout
@@ -6505,25 +6203,32 @@ with rotation variables
<param name="CylinderMaxX">0.960468635615</param>
\end_layout
-\begin_layout LyX-Code
- <param name="RadiusCylinder">3.35</param>
-\end_layout
-
-\end_deeper
-\begin_layout Standard
-A worked example is in input/cookbook/viscous_deformed_bottom.xml.
- Figure shows the strain rate invariant and velocity.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-
-\end_layout
+\end_deeper
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+A worked example is in
+\family typewriter
+input/cookbook/viscous_deformed_bottom.xml
+\family default
+.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Strain-deformed-bottom"
+
+\end_inset
+
+ shows the strain rate invariant and velocity.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
\begin_layout Plain Layout
\align center
@@ -6548,6 +6253,313 @@ name "fig:Strain-deformed-bottom"
\end_inset
Strain rate invariant and velocity for a deformed bottom boundary
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tracers-cookbook"
+
+\end_inset
+
+Tracers
+\end_layout
+
+\begin_layout Standard
+This example adds tracer particles to track where material moves.
+ These tracers play no active part in the simulation, only observing the
+ fields as they follow the movements of the material.
+\end_layout
+
+\begin_layout Enumerate
+Copy
+\family typewriter
+myviscous_deformed_bottom.xml
+\family default
+ to
+\family typewriter
+tracers.xml
+\family default
+.
+\end_layout
+
+\begin_layout Enumerate
+Add the components
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="pLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ManualParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="totalInitialParticles">1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="manualParticlePositions">
+\end_layout
+
+\begin_layout LyX-Code
+ <asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "x" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "y" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "z" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.3 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.6 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.9 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.3 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.6 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.9 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ </asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="passiveSwarmMovementHandler">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type"> ParticleMovementHandler </param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="passiveTracerSwarm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialPointsSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CellLayout">elementCellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ParticleLayout">pLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FiniteElement_Mesh">linearMesh</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="ParticleCommHandlers">
+\end_layout
+
+\begin_layout LyX-Code
+ <param> passiveSwarmMovementHandler </param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="passiveTracerAdvect">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SwarmAdvector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">passiveTracerSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityField">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="swarmOutput">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">TracerOutput</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">passiveTracerSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="PressureField">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Fields">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>VelocityMagnitudeField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>StrainRateInvariantField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Increase the number of timesteps so that we can see nice tracks by changing
+ the line
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<param name="maxTimeSteps">10</param>
+\end_layout
+
+\begin_layout Standard
+to
+\end_layout
+
+\begin_layout LyX-Code
+<param name="maxTimeSteps">100</param>
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+After running this input file you will see eight new files in the output
+ directory:
+\family typewriter
+swarmOutput.00000.dat
+\family default
+, ...
+
+\family typewriter
+swarmOutput.00007.dat
+\family default
+.
+ Inside each of these files is a record of the time position, pressure,
+ velocity magnitude, and strain-rate invariant that each particle saw as
+ it traveled along.
+ Plotting the particle tracks of all of these tracers gives us Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Particle-tracks-of"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename images/tracers.png
+ width 70col%
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:Particle-tracks-of"
+
+\end_inset
+
+Particle tracks of tracers
\end_layout
\end_inset
@@ -9164,234 +9176,6 @@ The parameters passed to this method pro
currently being evaluated, and the material point's elemental coordinates.
\end_layout
-\begin_layout Section
-Standard Condition Functions
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Standard-Condition-Functions-modify"
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-If you need to write your own Standard Condition Functions (see Section
-
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Standard-Condition-Functions"
-
-\end_inset
-
-), then the easiest way is to copy and paste an existing function.
- For example, suppose you wanted to create a function
-\family typewriter
-xSquared
-\family default
- that returns
-\begin_inset Formula $Ax^{2}$
-\end_inset
-
-, where A is a constant provided in the input file.
- You start by opening the file
-\end_layout
-
-\begin_layout LyX-Code
-src/StgFEM/plugins/StandardConditionFunctions/StandardConditionFunctions.c
-\end_layout
-
-\begin_layout Standard
-and finding the function
-\end_layout
-
-\begin_layout LyX-Code
-StgFEM_StandardConditionFunctions_Extension
-\end_layout
-
-\begin_layout Standard
-Make a copy of that function and rename it to
-\end_layout
-
-\begin_layout LyX-Code
-StgFEM_StandardConditionFunctions_xSquared
-\end_layout
-
-\begin_layout Standard
-Then you only need to modify the last 6 lines of the function to get the
- desired behavior.
- Specifically, it will become
-\end_layout
-
-\begin_layout LyX-Code
-void StgFEM_StandardConditionFunctions_xSquared( Node_LocalIndex node_lI,
-\end_layout
-
-\begin_layout LyX-Code
- Variable_Index var_I,
-\end_layout
-
-\begin_layout LyX-Code
- void* _context, void* _result
- ) {
-\end_layout
-
-\begin_layout LyX-Code
- DiscretisationContext* context = (DiscretisationContext*)_co
-ntext;
-\end_layout
-
-\begin_layout LyX-Code
- Dictionary* dictionary = context->dictionary;
-\end_layout
-
-\begin_layout LyX-Code
- FeVariable* feVariable = NULL;
-\end_layout
-
-\begin_layout LyX-Code
- FeMesh* mesh = NULL;
-\end_layout
-
-\begin_layout LyX-Code
- double* result = (double*) _result;
-\end_layout
-
-\begin_layout LyX-Code
- double* coord;
-\end_layout
-
-\begin_layout LyX-Code
- double factor;
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
- feVariable = (FeVariable*)FieldVariable_Register_GetByName(
-\end_layout
-
-\begin_layout LyX-Code
- context->fieldVariable_Register, "VelocityFiel
-d" );
-\end_layout
-
-\begin_layout LyX-Code
- mesh = feVariable->feMesh;
-\end_layout
-
-\begin_layout LyX-Code
- /* Find Centre of Solid Body Rotation */
-\end_layout
-
-\begin_layout LyX-Code
- factor = Dictionary_GetDouble_WithDefault( dictionary, "xSquaredFactor",
- 1.0 );
-\end_layout
-
-\begin_layout LyX-Code
- /* Find coordinate of node */
-\end_layout
-
-\begin_layout LyX-Code
- coord = Mesh_GetVertex( mesh, node_lI );
-\end_layout
-
-\begin_layout LyX-Code
- *result = factor * (coord[ I_AXIS ]*coord[ I_AXIS ];
-\end_layout
-
-\begin_layout LyX-Code
-}
-\end_layout
-
-\begin_layout Standard
-Then you need to register your function at the top of the file.
- After the lines
-\end_layout
-
-\begin_layout LyX-Code
-condFunc = ConditionFunction_New( StgFEM_StandardConditionFunctions_Extension,
-\end_layout
-
-\begin_layout LyX-Code
- "Velocity_Extension" );
-\end_layout
-
-\begin_layout LyX-Code
-ConditionFunction_Register_Add( context->condFunc_Register, condFunc );
-\end_layout
-
-\begin_layout Standard
-add the lines
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
-condFunc = ConditionFunction_New( StgFEM_StandardConditionFunctions_xSquared,
- "xSquared" );
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
-ConditionFunction_Register_Add( context->condFunc_Register, condFunc );
-\end_layout
-
-\begin_layout Standard
-The last thing to do is to modify
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
-src/StgFEM/plugins/StandardConditionFunctions/StandardConditionFunctions.h
-\end_layout
-
-\begin_layout Standard
-After the line
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
-void StgFEM_StandardConditionFunctions_Extension( Node_LocalIndex node_lI,
- Variable_Index var_I,
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
- void* _context, void*
- _result ) ;
-\end_layout
-
-\begin_layout Standard
-add the line
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
-void StgFEM_StandardConditionFunctions_xSquared( Node_LocalIndex node_lI,
- Variable_Index var_I,
-\end_layout
-
-\begin_layout LyX-Code
-
-\size small
- void* _context, void* _result
- ) ;
-\end_layout
-
-\begin_layout Standard
-Now recompile the code, and you should be able to use your new function
- from input files.
-\end_layout
-
\begin_layout Chapter
\start_of_appendix
Input File Format
@@ -17154,7 +16938,7 @@ You can also set the velocity to a funct
\end_layout
\begin_layout LyX-Code
- <param name="value">Gaussian</param>
+ <param name="value">Equation1</param>
\end_layout
\begin_layout LyX-Code
@@ -17178,24 +16962,12 @@ You can also set the velocity to a funct
\end_layout
\begin_layout LyX-Code
-<param name="GaussianHeight">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="GaussianWidth">0.1</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="GaussianCenter">0.5</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="GaussianDim">0</param>
-\end_layout
-
-\begin_layout Standard
-Note that the parameters are separated out into the variables section (see
- Section
+<param name="Equation1">exp(-((x-0.5)/0.1)^2)</param>
+\end_layout
+
+\begin_layout Standard
+Note that the equation string is separated out into the variables section
+ (see Section
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Variables"
@@ -17203,8 +16975,7 @@ reference "sub:Variables"
\end_inset
).
- In general, you can use any of the Standard Condition Functions (see Section
-
+ In general, you can use either an equation or file input (see Section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Standard-Condition-Functions"
@@ -17413,15 +17184,18 @@ reference "sub:Components"
\end_layout
\begin_layout Standard
-You can also use the Standard Condition Functions (see Section
+You can also use an equation or file input (see Section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Standard-Condition-Functions"
\end_inset
-), but due to technical issues, you must list Standard Condition Functions
- before StressBC in the list of components.
+), but due to technical issues, you must list a
+\family typewriter
+StgFEM_StandardConditionFunctions
+\family default
+ component before StressBC in the list of components.
So, for example, to add a stress condition to the left wall with a Gaussian
shape, the complete list of components would be
\end_layout
@@ -17495,7 +17269,7 @@ reference "sec:Standard-Condition-Functi
\end_layout
\begin_layout LyX-Code
- <param name="x_value">Gaussian</param>
+ <param name="x_value">Equation1</param>
\end_layout
\begin_layout LyX-Code
@@ -17518,19 +17292,7 @@ Gaussian
\end_layout
\begin_layout LyX-Code
-<param name="GaussianHeight">1.0</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="GaussianWidth">0.1</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="GaussianCenter">0.5</param>
-\end_layout
-
-\begin_layout LyX-Code
-<param name="GaussianDim">0</param>
+<param name="Equation1">exp(-((x-0.5)/0.1)^2)</param>
\end_layout
\begin_layout Standard
@@ -19226,332 +18988,149 @@ reference "sub:Hydrostatic-Pressure"
\end_inset
.
- It can subtract out the pressure from a two layer model with a temperature
- profile described by
-\family typewriter
-the TemperatureProfile
-\family default
- standard condition function (see Section
+ You give it the equations for the density and pressure.
+ Section
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Standard-Condition-Functions"
\end_inset
-).
- Specifically, it subtracts out a density given by
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula \[
-\begin{array}{cc}
-0 & x>height\\
-upperDensity\cdot\left(1-upperAlpha\cdot T\right) & materialBoundary>x>height\\
-lowerDensity\cdot\left(1-lowerAlpha\cdot T\right) & x>materialBoundary\end{array},\]
-
-\end_inset
-
- where
-\end_layout
-
-\begin_layout Standard
-\align left
-\begin_inset Formula \[
-T=\left\{ \begin{array}{cc}
-T\_0 & x>height\\
-T\_0+linearCoefficient\left(height-x\right) & x<height\\
-+exponentialCoefficient1\left(1-\exp\left(-exponentialCoefficient2\left(height-x\right)\right)\right)\end{array}\right..\]
-
-\end_inset
-
- This component also computes a pressure by integrating this density profile
- analytically and multiplying by
-\begin_inset Formula $gravity.$
-\end_inset
-
- Once you have created a
-\family typewriter
-HydrostaticTerm
-\family default
-, you have to remember to pass it along to
-\family typewriter
-BuoyancyForceTerm
-\family default
- (Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:BouyancyForceTerm"
-
-\end_inset
-
-) and a
-\family typewriter
-StressBC
-\family default
- (Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Stress-Boundary-Conditions"
-
-\end_inset
-
-) in order for it to take effect.
- You also have to pass it to any
-\family typewriter
-DruckerPrager
-\family default
- rheologies (Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:DruckerPrager"
-
-\end_inset
-
-) that you are using, so that the rheology will have the correct pressure.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="12" columns="2">
-<features>
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Defaults
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-upperDensity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-upperAlpha
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-lowerDensity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-lowerAlpha
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-height
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-materialBoundary
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-T_0
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-linearCoefficient
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-exponentialCoefficient1
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-exponentialCoefficient2
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-gravity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
+ has complete details on how to enter those equations.
+ As an example, consider the case where the material has a density of 5,
+ going from the bottom to a height of 13, with a gravity of 10.
+ The
+\family typewriter
+densityEquation
+\family default
+ would then be
+\end_layout
+
+\begin_layout LyX-Code
+step(13-y)*5
+\end_layout
+
+\begin_layout Standard
+and the
+\family typewriter
+pressureEquation
+\family default
+ would be the integral of that, multiplied by the gravity
+\end_layout
+
+\begin_layout LyX-Code
+step(13-y)*5*step(13-y)*10
+\end_layout
+
+\begin_layout Standard
+If you have temperature and thermal expansity in your problem, remember
+ to put those effects in.
+ So if the temperature is a linear gradient from 0 at the top to 1 at the
+ bottom, and your thermal expansity is
+\begin_inset Formula $10^{-5}$
+\end_inset
+
+, then the
+\family typewriter
+densityEquation
+\family default
+ would be
+\end_layout
+
+\begin_layout LyX-Code
+step(13-y)*5*(1-(10^(-5))*(13-y)/13)
+\end_layout
+
+\begin_layout Standard
+and the
+\family typewriter
+pressureEquation
+\family default
+ would be the integral of this multiplied by gravity, with the boundary
+ condition that the pressure is 0 at the surface
+\end_layout
+
+\begin_layout LyX-Code
+step(13-y)*5*((13-y) - (10^(-5))*((13-y)^2)/26)*10
+\end_layout
+
+\begin_layout Standard
+The integral for the pressure, in particular, may become very tricky.
+ If your setup defies simple analytic treatments, it may be ok to use simpler,
+ approximate density and temperature.
+ However, it is
+\series bold
+\color red
+critical
+\series default
+\color inherit
+ that the pressure is always the integral of the density.
+ Otherwise, you will get wrong results.
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+densityEquation
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+pressureEquation
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
\end_layout
\end_inset
@@ -20121,7 +19700,7 @@ force_value If ``force_type'' is ``doubl
\end_layout
\begin_layout Section
-Standard Condition Functions
+Equation Input
\begin_inset CommandInset label
LatexCommand label
name "sec:Standard-Condition-Functions"
@@ -20132,542 +19711,1623 @@ name "sec:Standard-Condition-Functions"
\end_layout
\begin_layout Standard
-Standard Condition Functions are functions that you can use to specify initial
- conditions and boundary conditions.
- At present, they take in a coordinate
-\begin_inset Formula $(x,y,z)$
-\end_inset
-
- and output a function
-\begin_inset Formula $f(x,y,z)$
-\end_inset
-
-.
- They are all defined in the directory
-\family typewriter
-src/StgFEM/plugins/StandardConditionFunctions/
-\family default
-.
- For the following descriptions, the sides of the box are at
-\begin_inset Formula $x_{min}$
-\end_inset
-
- and
-\begin_inset Formula $x_{max}$
-\end_inset
-
-, and
-\begin_inset Formula $L\equiv x_{max}-x_{min}$
-\end_inset
-
-, and all names with CamelCase capitalization are variables from the input
- file.
- If you need to write your own function, see Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Standard-Condition-Functions-modify"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Description
-Velocity_SolidBodyRotation Returns the coordinates rotated by
-\family typewriter
-SolidBodyRotationOmega
-\family default
- around the
-\begin_inset Formula $z$
-\end_inset
-
- axis, centered at the coordinate (
-\family typewriter
-SolidBodyRotationCentreX
-\family default
-,
-\family typewriter
-SolidBodyRotationY
-\family default
-), out to a radius
-\family typewriter
-RadiusCylinder
-\family default
-.
- Specifically, if
-\begin_inset Formula $r<RadiusCylinder$
-\end_inset
-
-
-\begin_inset Formula \[
-\begin{array}{ccc}
-f(x,y,z)_{x} & = & -SolidBodyRotationOmega(y-SolidBodyRotationCentreY)\\
-f(x,y,z)_{y} & = & SolidBodyRotationOmega(x-SolidBodyRotationCentreX)\end{array},\]
-
-\end_inset
-
- otherwise returns 0.
-\end_layout
-
-\begin_layout Description
-Velocity_PartialRotationX Returns the
-\emph on
-
-\begin_inset Formula $x$
-\end_inset
-
-
-\emph default
- component of Velocity_SolidBodyRotation.
-\end_layout
-
-\begin_layout Description
-Velocity_PartialRotationY Returns the
-\begin_inset Formula $y$
-\end_inset
-
- component of Velocity_SolidBodyRotation.
-\end_layout
-
-\begin_layout Description
-TaperedRotationX If
-\begin_inset Formula $r<RadiusCylinder$
-\end_inset
-
-, returns Velocity_PartialRotationX.
- If
-\begin_inset Formula $RadiusCylinder<r<TaperedRadius$
-\end_inset
-
-, returns
-\begin_inset Formula \[
-VelocityPartialRotationX\left(\frac{TaperedRadius-r}{TaperedRadius-RadiusCylinder}\right).\]
-
-\end_inset
-
- If
-\begin_inset Formula $r>TaperedRadius$
-\end_inset
-
-, returns 0.
-\end_layout
-
-\begin_layout Description
-TaperedRotationY Similar to TaperedRotationX, but returns Velocity_PartialRotati
-onY.
-\end_layout
-
-\begin_layout Description
-Velocity_SimpleShear
-\begin_inset Formula $f(x,y,z)=SimpleShearFactor\left(y-SimpleShearCentreY\right)$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-Velocity_Extension
-\begin_inset Formula $f(x,y,z)=ExtensionFactor\left(x-ExtensionCentreX\right)$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-Velocity_PartialLid_TopLayer Returns 0 if the
-\begin_inset Formula $x$
-\end_inset
-
- coordinate is within one grid point of the boundary; 1 otherwise.
-\end_layout
-
-\begin_layout Description
-Velocity_LinearInterpolationLid
-\begin_inset Formula \[
-f(x,y,z)=bcLeftHandSideValue+\left(\frac{bcRightHandSideValue-bcLeftHandSideValue}{L}\right)x\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-Velocity_Lid_RampWithCentralMax
-\begin_inset Formula $f(x,y,z)=\left\{ \begin{array}{cc}
-2\left(x-x_{min}\right)/L & x<L/2+x_{min}\\
-1-2(x-x_{min}-L/2) & x>L/2+x_{min}\end{array}\right.$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-Velocity_SinusoidalLid
-\begin_inset Formula \[
-f(x,y,z)=\sin\left(\frac{\pi\left(x-x_{min}\right)}{L}sinusoidalLidWavenumber\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-Velocity_Lid_CornerOnly Returns 1 if the coordinate is on the right boundary.
-\end_layout
-
-\begin_layout Description
-Temperature_CosineHill Returns a hill defined by a cosine.
- Specifically, if we define pre-rotated coordinates
-\begin_inset Formula \[
-\begin{array}{ccc}
-x_{pre-rotate} & = & CosineHillCentreX-SolidBodyRotationCentreX\\
-y_{pre-rotate} & = & CosineHillCentreY-SolidBodyRotationCentreY\\
-z_{pre-rotate} & = & CosineHillCentreZ-SolidBodyRotationCentreZ\end{array},\]
-
-\end_inset
-
- and then rotate them around the
-\begin_inset Formula $z$
-\end_inset
-
- axis by the angle
-\begin_inset Formula $\theta=SolidBodyRotationOmega*t$
-\end_inset
-
-
-\begin_inset Formula \[
-\begin{array}{ccc}
-x_{hill} & = & x_{pre-rotate}\cos\theta-y_{pre-rotate}\sin\theta\\
-y_{hill} & = & x_{pre-rotate}\sin\theta+y_{pre-rotate}\cos\theta\\
-z_{hill} & = & z_{pre-rotate}\end{array},\]
-
-\end_inset
-
- then
-\begin_inset Formula \[
-f(x,y,z)=\left\{ \begin{array}{cc}
-\frac{CosineHillHeight}{4}\cos\left(\frac{2\pi r}{CosineHillDiameter}\right) & r<CosineHillDiameter\\
-0 & r>CosineHillDiameter\end{array}\right.,\]
-
-\end_inset
-
- where
-\begin_inset Formula $r$
-\end_inset
-
- is the distance from the center of the hill
-\begin_inset Formula \[
-r\equiv\sqrt{\left(x-x_{hill}\right)^{2}+\left(y-y_{hill}\right)^{2}+\left(z-z_{hill}\right)^{2}}.\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-LinearWithSinusoidalPerturbation If you scale the
-\begin_inset Formula $y$
-\end_inset
-
- coordinate
-\begin_inset Formula \[
-y_{scaled}=\frac{\left(y-SinusoidalTempIC\_BottomLayerCoord\right)}{SinusoidalTempIC\_TopLayerCoord-SinusoidalTempIC\_BottomLayerCoord},\]
-
-\end_inset
-
-then this returns
-\begin_inset Formula \[
-\begin{array}{ccc}
-f(x,y,z) & = & SinusoidalTempIC\_TopLayerBC\\
- & & -\left(SinusoidalTempIC\_TopLayerBC-SinusoidalTempIC\_BottomLayerBC\right)\left(1-y_{scaled}\right)\\
- & & +SinusoidalTempIC\_PerturbationAmplitude\\
- & & *\left(\cos\left(\pi x_{scaled}*SinusoidalTempIC\_HorizontalWaveNumber\right)\right.\\
- & & *\left.sin\left(\pi y_{scaled}SinusoidalTempIC\_VerticalWaveNumber\right)\right)\end{array}.\]
-
-\end_inset
-
-if
-\begin_inset Formula $0\leq y_{scaled}\leq1$
-\end_inset
-
-, and 0 otherwise.
-\end_layout
-
-\begin_layout Description
-Temperature_Trigonometry
-\begin_inset Formula \[
-f(x,y,z)=1-\frac{\pi y}{2}\sin\left(\frac{\pi x}{x_{max}-x_{min}}\right).\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-VelicTemperatureIC
-\begin_inset Formula \[
-f(x,y,z)=sigma*\cos\left(\pi wavenumberX\left(\frac{x-x_{min}}{x_{max}-x_{min}}\right)\right)\sin\left(\pi\left(y-y_{min}\right)wavenumberY\right),\]
-
-\end_inset
-
-where the height of the box is constrained to
-\begin_inset Formula $y_{max}-y_{min}=1$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Description
-VelicTemperatureIC_SolB
-\begin_inset Formula \[
-f(x,y,z)=sigma*\cos\left(\pi wavenumberX\left(\frac{x-x_{min}}{x_{max}-x_{min}}\right)\right)\sinh\left(\pi wavenumberY\left(\frac{y-y_{min}}{x-x_{min}}\right)\right),\]
-
-\end_inset
-
-where the height of the box is constrained to
-\begin_inset Formula $y_{max}-y_{min}=1$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Description
-AnalyticalTemperatureIC First, define
-\begin_inset Formula \[
-\begin{array}{ccc}
-x_{0} & \equiv & x-x_{min}\\
-y_{0} & \equiv & y-y_{min}\\
-L & \equiv & x_{max}-x_{min}\\
-H & \equiv & y_{max}-y_{min}\\
-\lambda & \equiv & L/H\end{array},\]
-
-\end_inset
-
-and then compute some intermediate quantities
-\begin_inset Formula \[
-\begin{array}{ccc}
-u_{0} & = & \frac{\lambda^{7/3}}{\left(1+\lambda^{4}\right)^{2/3}}\left(\frac{Ra}{2\sqrt{pi}}\right)^{2/3}\\
-v_{0} & = & u_{0}/\lambda\\
-Q & = & 2\sqrt{\lambda/\left(\pi u_{0}\right)}\\
-T_{u} & = & \frac{1}{2}erf(\left(\frac{1}{2}\left(1-y_{0}\right)\sqrt{u_{0}/x_{0}}\right)\\
-T_{l} & = & 1-\frac{1}{2}erf\left(\frac{1}{2}y_{0}\sqrt{u_{0}/\left(\lambda-x_{0}\right)}\right)\\
-T_{r} & = & \frac{1}{2}+\frac{1}{2}\left(Q/\sqrt{\pi}\right)\sqrt{v_{0}/\left(y_{0}+1\right)}\exp\left(-x_{0}^{2}v_{0}/\left(4y_{0}+4\right)\right)\\
-T_{s} & = & \frac{1}{2}-\frac{1}{2}\left(Q/\sqrt{\pi}\right)\sqrt{v_{0}/\left(2-y_{0}\right)}\exp\left(-\left(\lambda-x_{0}\right)^{2}v_{0}/\left(8-4y_{0}\right)\right)\\
-g & = & T_{u}+T_{l}+T_{r}+T_{s}-1.5\end{array}.\]
-
-\end_inset
-
- The result is
-\begin_inset Formula \[
-f(x,y,z)=\left\{ \begin{array}{cc}
-0 & g<0\\
-g & 0<g<1\\
-1 & g>1\end{array}\right..\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-SinusoidalExtension
-\begin_inset Formula \[
-\begin{array}{ccc}
-f(x,y,z) & = & SinusoidalExtensionVelocity+SinusoidalExtensionAmplitude\\
- & & *\cos\left(2\pi SinusoidalExtensionFrequency\left(t+dt-SinusoidalExtensionPhaseShift\right)\right)\end{array}\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-StepFunction This function returns a ramp function in the axis prescribed
- by the integer
-\begin_inset Formula $StepFunctionDim$
-\end_inset
-
-, where
-\begin_inset Formula $0\Rightarrow x$
-\end_inset
-
-,
-\begin_inset Formula $1\Rightarrow y$
-\end_inset
-
-,
-\begin_inset Formula $2\Rightarrow z$
-\end_inset
-
-.
- You can also define a step function in time with by setting
-\begin_inset Formula $StepFunctionDim=3$
-\end_inset
-
-.
- Defining some convenient constants
-\begin_inset Formula \[
-\begin{array}{ccc}
-w & = & coord[dim]\\
-w_{-} & = & StepFunctionLowerOffset\\
-w_{+} & = & StepFunctionUpperOffset\\
-V_{-} & = & StepFunctionLowerValue\\
-V_{+} & = & StepFunctionUpperValue\end{array},\]
-
-\end_inset
-
+The main way to enter initial conditions and boundary conditions is via
+
+\family typewriter
+Equation
+\family default
+'s.
+ These are strings that get interpreted at runtime.
+ You can have up to 10 different
+\family typewriter
+Equation
+\family default
+'s at a time:
+\family typewriter
+Equation1
+\family default
+,
+\family typewriter
+Equation2
+\family default
+, ...
+
+\family typewriter
+Equation10
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The syntax is meant to be as close as possible to natural notation as possible.
+ For example,
+\end_layout
+
+\begin_layout LyX-Code
+exp(-2*(x^2 + y^2))
+\end_layout
+
+\begin_layout Standard
+is equivalent to the formula
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+e^{-2\left(x^{2}+y^{2}\right)}.\]
+
+\end_inset
+
+Within each equation, the coordinates are the only predefined variables:
+
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+,
+\family typewriter
+z
+\family default
+,
+\family typewriter
+t
+\family default
+.
+ For your convenience, you can also define variables within an equation.
+ The equation
+\end_layout
+
+\begin_layout LyX-Code
+r=hypot(x^2+y^2), r*exp(-(r/10)^2)
+\end_layout
+
+\begin_layout Standard
+defines a radius and then uses it.
+ Statements are separated by commas
+\begin_inset Quotes sld
+\end_inset
+
+,
+\begin_inset Quotes srd
+\end_inset
+
+, and the return value of the equation is the last statement.
+\end_layout
+
+\begin_layout Standard
+Gale uses muParser
+\begin_inset Flex URL
+status open
+
+\begin_layout Plain Layout
+
+http://muParser.sf.net
+\end_layout
+
+\end_inset
+
+, with some minor modifications, to handle the actual parsing.
+ The available unary and binary operators are
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
++
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+addition
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+subtraction or unary minus
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+*
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+multiplication
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+/
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+division
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+^
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+raise to the power:
+\begin_inset Formula $x^{y}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In addition, the available functions are
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="34" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sin(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sin
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cos(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cos
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+tan(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+tan
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+asin(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+arcsin
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+acos(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+arccos
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+atan(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+arctan
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sinh(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hyperbolic sin
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cosh(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hyperbolic cos
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+tanh(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hyperbolic tan
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+asinh(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hyperbolic arcsin
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+acosh(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hyperbolic arccos
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+atanh(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hyperbolic arctan
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cbrt(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+cube root:
+\begin_inset Formula $\sqrt[3]{x}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+copysign(x,y)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+return the value of x with the sign of y
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+erf(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+error function
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+erfc(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+complementary error function
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+expm1(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $e^{x}-1$
+\end_inset
+
+, optimised for when x is small
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+hypot(x,y)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqrt{x^{2}+y^{2}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+lgamma(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+natural log of the absolute value of the gamma function
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+log1p(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\log\left(1+x\right)$
+\end_inset
+
+, optimised for when x is small
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+remainder(x,y)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+the remainder of x/y
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+rint(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+round to the nearest int
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+gamma(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Gamma function
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+log10(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\log_{10}\left(x\right)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+ln(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+natural logarithm:
+\begin_inset Formula $\log\left(x\right)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+exp(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $e^{x}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+abs(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Absolute value:
+\begin_inset Formula $|x|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sqrt(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Square root:
+\begin_inset Formula $\sqrt{x}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sign(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+-1 if x<0, +1 if x>0 and 0 if x==0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+step(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0 if x<0, 1 otherwise
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+sum(x1,x2,x3,...)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Sum of individual values: x1+x2+x3+...
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+avg(x1,x2,x3,...)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Average of all values: (x1+x2+x3+...)/num_values
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+min(x1,x2,x3,...)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Minimum of all values
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+max(x1,x2,x3,...)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Maximum of all values
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In addition, you can use the function
+\family typewriter
+if(a,b,c)
+\family default
+.
+ If the first element
+\family typewriter
+a
+\family default
+ is true, then return
+\family typewriter
+b
+\family default
+.
+ Otherwise return
+\family typewriter
+c
+\family default
+.
+ For the condition
+\family typewriter
+a
+\family default
+, you can use all of the normal relational operators.
+ Unfortunately, because the equations are embedded in an XML file, you are
+ not allowed to use the characters
+\begin_inset Quotes sld
+\end_inset
+
+<
+\begin_inset Quotes srd
+\end_inset
+
+ or
+\begin_inset Quotes sld
+\end_inset
+
+>
+\begin_inset Quotes srd
+\end_inset
+
+.
+ Instead, you must use the escaped versions
+\begin_inset Quotes sld
+\end_inset
+
+<
+\begin_inset Quotes srd
+\end_inset
+
+ and
+\begin_inset Quotes sld
+\end_inset
+
+>
+\begin_inset Quotes srd
+\end_inset
+
+.
+ To be specific, the allowed relational operators are
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+<
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+less than
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+<=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+less than or equal
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+>
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+greater than
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+>=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+greater than or equal
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+==
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+is equal
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+!=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+is not equal
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+||
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+logical or
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+&&
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+logical and
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+So the expression
+\end_layout
+
+\begin_layout LyX-Code
+if(x<1, 7, 13)
+\end_layout
+
+\begin_layout Standard
+must be written as
+\end_layout
+
+\begin_layout LyX-Code
+if(x < 1, 7, 13)
+\end_layout
+
+\begin_layout Standard
+Most of the time, you can use the
+\family typewriter
+step
+\family default
+ function instead
+\end_layout
+
+\begin_layout LyX-Code
+7 + step(x-1)*6
+\end_layout
+
+\begin_layout Standard
+Note that rounding issues may make it dangerous to write it as
+\end_layout
+
+\begin_layout LyX-Code
+step(1-x)*7 + step(x-1)*13
+\end_layout
+
+\begin_layout Standard
+since, in the general case, depending on roundoff, both parts may be true.
+ This would yield 20 instead of 7 or 13.
+ The
+\family typewriter
+if()
+\family default
+ function is also useful if one of the results is very expensive to compute.
+ For example, given the statement
+\end_layout
+
+\begin_layout LyX-Code
+if(x < 1, 0, expensive_function)
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+expensive_function
+\family default
+ will only be evaluated if
+\begin_inset Formula $x\geq1$
+\end_inset
+
+.
+ If you used
+\family typewriter
+step
+\family default
+,
+\family typewriter
+expensive_function
+\family default
+ would always be evaluated.
+\end_layout
+
+\begin_layout Standard
+Finally, you can use the syntax
+\family typewriter
+?:
+\family default
+ as an exact replacement for
+\family typewriter
+if()
+\family default
+.
+ So for the example given above,
+\end_layout
+
+\begin_layout LyX-Code
+(x < 1) ? 0 : expensive_function
+\end_layout
+
+\begin_layout Standard
+produces the same result, including only evaluating
+\family typewriter
+expensive_function
+\family default
if
-\begin_inset Formula $StepFunctionLessThan$
-\end_inset
-
- is
-\family typewriter
-True
-\family default
-, then
-\begin_inset Formula \[
-f(x,y,z)=\left\{ \begin{array}{cc}
-V_{-} & w<w_{-}\\
-V_{-}+\left(V_{+}-V_{-}\right)\left(\frac{w-w_{-}}{w_{+}-w_{-}}\right) & w_{-}<w<w_{+}\\
-V_{+} & w_{+}<w\end{array}\right.,\]
-
-\end_inset
-
- otherwise it is reversed
-\begin_inset Formula \[
-f(x,y,z)=\left\{ \begin{array}{cc}
-V_{+} & w<w_{-}\\
-V_{-}+\left(V_{+}-V_{-}\right)\left(\frac{w_{+}-w}{w_{+}-w_{-}}\right) & w_{-}<w<w_{+}\\
-V_{-} & w_{+}<w\end{array}\right.,\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-StepFunctionProduct1 Using a similar scheme as StepFunction to specify the
- dimension with
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Formula $StepFunctionProduct1Dim$
-\end_inset
-
-,
-\begin_inset Formula \[
-f(x,y,z)=\left\{ \begin{array}{cc}
-0 & w<StepFunctionProduct1Start\\
-StepFunctionProduct1Value & StepFunctionProduct1Start<w<StepFunctionProduct1End\\
-0 & w>StepFunctionProduct1End\end{array}\right.\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-StepFunctionProduct2
-\end_layout
-
-\begin_layout Description
-StepFunctionProduct3
-\end_layout
-
-\begin_layout Description
-StepFunctionProduct4 These are the same as StepFunctionProduct1 except that
- they use different variables (e.g.,
-\begin_inset Formula $StepFunctionProduct2Dim$
-\end_inset
-
- instead of
-\begin_inset Formula $StepFunctionProduct1Dim$
-\end_inset
-
-).
-\end_layout
-
-\begin_layout Description
-Gaussian
-\begin_inset Formula \[
-f(x,y,z)=\left(GaussianHeight\right)\exp\left[-\left(\frac{GaussianCenter-coord[GaussianDim]}{GaussianWidth}\right)^{2}\right]\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-TemperatureProfile
-\begin_inset Formula \[
-f(x,y,z)=\left\{ \begin{array}{cc}
-T_{0} & y>maxY\\
-T_{0}+A\left(maxY-y\right)+B\left(1-\exp\left(-C\left(maxY-y\right)\right)\right) & y<maxY,H_{0}<0\\
-\min\left(T_{m},T_{0}+\frac{\left(T_{m}-T_{0}\right)}{H}\left(maxY-y\right)+B\left(1-\exp\left(-C\left(maxY-y\right)\right)\right)\right) & y<maxY,H_{0}>0\end{array}\right.,\]
-
-\end_inset
-
- where
-\begin_inset Formula \[
-H=\min\left(H_{m},H_{o}+2dH\left|x-x_{c}\right|/\left(maxX-minX\right)\right),\]
-
-\end_inset
-
- and
-\begin_inset Formula \begin{eqnarray*}
-T_{0} & \equiv & TemperatureProfileTop,\\
-A & \equiv & TemperatureLinearCoefficient,\\
-B & \equiv & TemperatureExponentialCoefficient1,\\
-C & \equiv & TemperatureExponentialCoefficient2,\\
-T_{m} & \equiv & TemperatureProfileMax,\\
-H_{0} & \equiv & TemperatureProfileH0,\\
-H_{m} & \equiv & TemperatureProfileHm,\\
-dH & \equiv & TemperatureProfiledH,\\
-x_{c} & \equiv & ExtensionCentreX.\end{eqnarray*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Description
-File1,...,File10 This reads
+\begin_inset Formula $x\geq1$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+File Input Data
+\end_layout
+
+\begin_layout Standard
+The other way to set initial and boundary conditions is by reading it in
+ from a file.
+ You can use up to 10 different files as input data (
+\family typewriter
+File1
+\family default
+,
+\family typewriter
+File2
+\family default
+, ...
+
+\family typewriter
+File10
+\family default
+).
+ For each
+\family typewriter
+File
+\family default
+, there are a number of associated parameters.
+ As a concrete example,
+\family typewriter
+File1
+\family default
+ will have data along the axis
+\family typewriter
+File1_dim
+\family default
+ and, if defined, the axes
+\family typewriter
+File1_dim2
+\family default
+ and
+\family typewriter
+File1_dim3
+\family default
+.
+ Depending on how many dimensions are defined,
+\family typewriter
+File1
+\family default
+ will be an array of
\family typewriter
File1_N
\family default
- elements from
-\family typewriter
-File1_Name
-\family default
-.
- The format is two columns, with the first column being the coordinate along
- the direction
-\family typewriter
-File1_Dim
-\family default
- and the second being the value.
+,
+\family typewriter
+File1_N*File1_N2
+\family default
+, or
+\family typewriter
+File1_N*File1_N2*File1_N3
+\family default
+ elements.
+ Gale reads these elements from a file.
+ The format of the file is one column for each of the coordinates (1, 2,
+ or 3), and one column for the value.
The coordinates must be sorted and increasing.
Gale linearly interpolates between values as necessary.
So a file with the two lines
\end_layout
-\begin_deeper
\begin_layout LyX-Code
\family typewriter
0 10
-\begin_inset Newline newline
-\end_inset
-
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
100 20
\end_layout
\begin_layout Standard
-will create a linear gradient between 0 and 100.
-\end_layout
-
-\end_deeper
+will create a linear gradient between 0 and 100, starting with 10 at 0 and
+ ending with 20 at 100.
+ For points less than 0, Gale uses the value of the lowest point (10).
+ For points greater than 100, Gale uses the value of the highest point (20).
+\end_layout
+
+\begin_layout Standard
+For 2D and 3D input files, the coordinate mesh defined by the input file
+ must be a rectangular grid.
+\end_layout
+
+\begin_layout Section
+Tracers
+\end_layout
+
+\begin_layout Standard
+You can add tracer particles to the simulation to help you track where material
+ is flowing.
+ The existing material particles are not suitable for that because they
+ may get duplicated or removed as the simulation proceeds.
+ This is necessary to keep the number of particles down to a reasonable
+ level.
+ Tracers, on the other hand, are merely silent observers, playing no role
+ in the evolution of the system.
+\end_layout
+
+\begin_layout Standard
+To add tracers to your simulation, first set the initial position of the
+ particles with a
+\family typewriter
+ManualParticleLayout
+\family default
+ component.
+ An example of one that puts down 8 tracers is
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="pLayout">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">ManualParticleLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="totalInitialParticles">1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="manualParticlePositions">
+\end_layout
+
+\begin_layout LyX-Code
+ <asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "x" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "y" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ <columnDefinition name = "z" type="double"/>
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.3 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.6 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.9 .1 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.0 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.3 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.6 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ 1.9 .2 .1
+\end_layout
+
+\begin_layout LyX-Code
+ </asciidata>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Then add some components to set up the mesh and time integration
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="passiveSwarmMovementHandler">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type"> ParticleMovementHandler </param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="passiveTracerSwarm">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialPointsSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="CellLayout">elementCellLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="ParticleLayout">pLayout</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FiniteElement_Mesh">linearMesh</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="FeMesh">mesh-linear</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="ParticleCommHandlers">
+\end_layout
+
+\begin_layout LyX-Code
+ <param> passiveSwarmMovementHandler </param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="passiveTracerAdvect">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">SwarmAdvector</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">passiveTracerSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityField">VelocityField</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Finally, add a swarmOutput component to output values of various fields
+ (e.g.
+ pressure, temperature) as the simulation progresses.
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="swarmOutput">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">TracerOutput</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Swarm">passiveTracerSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="PressureField">PressureField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Fields">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>VelocityMagnitudeField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>StrainRateInvariantField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Note that to output the pressure correctly with hydrostatic corrections,
+ you must use the
+\family typewriter
+PressureField
+\family default
+ variable slot.
+ All other fields are output by adding them to the
+\family typewriter
+Fields
+\family default
+ list.
+ You may add as many or as few scalar fields as you like to the
+\family typewriter
+Fields
+\family default
+ list.
+\end_layout
+
\begin_layout Section
\begin_inset CommandInset label
LatexCommand label
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