[cig-commits] r11392 - in long/3D/Gale/trunk: . documentation documentation/images

walter at geodynamics.org walter at geodynamics.org
Mon Mar 10 11:45:34 PDT 2008


Author: walter
Date: 2008-03-10 11:45:34 -0700 (Mon, 10 Mar 2008)
New Revision: 11392

Added:
   long/3D/Gale/trunk/documentation/images/Paraview_topography.png
   long/3D/Gale/trunk/documentation/images/Paraview_viscous_fixed.png
   long/3D/Gale/trunk/documentation/images/inflow_fixed.eps
   long/3D/Gale/trunk/documentation/images/inflow_fixed.fig
   long/3D/Gale/trunk/documentation/images/strainrate_1cm.png
   long/3D/Gale/trunk/documentation/images/tibet_setup.eps
   long/3D/Gale/trunk/documentation/images/tibet_setup.fig
   long/3D/Gale/trunk/documentation/images/topo_error.eps
   long/3D/Gale/trunk/documentation/images/topo_scaled_error.eps
Modified:
   long/3D/Gale/trunk/
   long/3D/Gale/trunk/documentation/gale.lyx
Log:
 r2025 at earth:  boo | 2008-03-10 11:38:52 -0700
 A whole host of doc updates



Property changes on: long/3D/Gale/trunk
___________________________________________________________________
Name: svk:merge
   - 3a629746-de10-0410-b17b-fd6ecaaa963e:/cig:2024
   + 3a629746-de10-0410-b17b-fd6ecaaa963e:/cig:2025

Modified: long/3D/Gale/trunk/documentation/gale.lyx
===================================================================
--- long/3D/Gale/trunk/documentation/gale.lyx	2008-03-10 18:45:31 UTC (rev 11391)
+++ long/3D/Gale/trunk/documentation/gale.lyx	2008-03-10 18:45:34 UTC (rev 11392)
@@ -1078,7 +1078,7 @@
 \end_layout
 
 \begin_layout Section
-Gale Usage
+Basic Usage
 \end_layout
 
 \begin_layout Standard
@@ -1263,32 +1263,103 @@
  directory.
 \end_layout
 
+\begin_layout Section
+Advanced Usage
+\end_layout
+
+\begin_layout Subsection
+Direct Solvers
+\end_layout
+
 \begin_layout Standard
-Gale uses PETSc's GMRES linear solver by default.
- However, PETSc has a facility where you can use command line arguments
- to change the solver.
- For example, on serial machines with small problems, a direct solve can
- be much faster than GMRES.
- To use a direct LU solve, you only need to append arguments to the command
- line
+If you have a problem with strong viscosity gradients, the default solver
+ (GMRES) may converge very slowly.
+ Strong viscosity gradients occur when you start with materials with different
+ viscosities (e.g.
+ Appendix 
+\begin_inset LatexCommand ref
+reference "sec:Circular-Inclusion"
+
+\end_inset
+
+, 
+\begin_inset LatexCommand ref
+reference "sec:Falling-Sphere"
+
+\end_inset
+
+, and 
+\begin_inset LatexCommand ref
+reference "sec:Falling-Cylinder"
+
+\end_inset
+
+), or when materials yield (e.g.
+ Appendix 
+\begin_inset LatexCommand ref
+reference "sec:Geomod-2004"
+
+\end_inset
+
+).
 \end_layout
 
+\begin_layout Standard
+One solution is to use a direct solver instead of GMRES.
+ PETSc has a facility where you can use command line arguments to change
+ the solver.
+ For example, on a single machine, to use a direct LU solve, you only need
+ to append arguments to the command line
+\end_layout
+
 \begin_layout LyX-Code
-./Gale-1_2_1  input/cookbook/yielding.xml -pc_type lu -ksp_type preonly
+./Gale-1_2_2  input/cookbook/yielding.xml -pc_type lu -ksp_type preonly
 \end_layout
 
 \begin_layout Standard
-You can also change the default values of 
+In parallel, the analogous approach would be to use Mumps, a parallel direct
+ solver.
+ You first need to make sure that your version of Petsc was installed with
+ Mumps.
+ If you built Petsc yourself, you need to the add the option 
+\begin_inset Quotes sld
+\end_inset
+
+
 \family typewriter
-yielding.xml
+--download-mumps=yes
 \family default
- without modifying that file by appending arguments.
+
+\begin_inset Quotes srd
+\end_inset
+
+ when configuring.
+ The Petsc installation on TACC Lonestar has been installed with Mumps.
+\end_layout
+
+\begin_layout Standard
+Once that is done, enabling it is again just appending a few arguments to
+ the command line
+\end_layout
+
+\begin_layout LyX-Code
+./Gale-1_2_2  input/cookbook/yielding.xml mat_type aijmumps -ksp_type pre
+ only -pc_type lu
+\end_layout
+
+\begin_layout Subsection
+Command line parameters
+\end_layout
+
+\begin_layout Standard
+You can also change the default values of the input file without modifying
+ that file by appending arguments.
  For example, to just change the number of time steps from the default value
  10 to 20, use the following command
 \end_layout
 
 \begin_layout LyX-Code
-./Gale-1_2_1  input/cookbook/yielding.xml --maxTimeSteps=20
+./Gale-1_2_2  input/cookbook/yielding.xml --maxTimeSteps=20
 \end_layout
 
 \begin_layout Standard
@@ -1298,10 +1369,48 @@
 \begin_layout LyX-Code
 
 \size small
-./Gale-1_2_1  input/cookbook/yielding.xml --maxTimeSteps=20 --dim=3 --elementResI=
+./Gale-1_2_2  input/cookbook/yielding.xml --maxTimeSteps=20 --dim=3 --elementResI=
 64 --elementResJ=64 --elementResK=64 --particlesPerCell=60 --dumpEvery=10
 \end_layout
 
+\begin_layout Subsection
+Parallel Issues
+\end_layout
+
+\begin_layout Standard
+When writing 
+\family typewriter
+.dat
+\family default
+ files in parallel (see Sections 
+\begin_inset LatexCommand ref
+reference "sec:.dat-ASCII-Files"
+
+\end_inset
+
+ and 
+\begin_inset LatexCommand ref
+reference "sec:.dat-Binary-Files"
+
+\end_inset
+
+), all of the processors have to cooperate.
+ This is because the 
+\family typewriter
+.dat
+\family default
+ files are single files that have information from every processor.
+ Gale uses file locking to ensure this cooperation.
+ But on some parallel file systems, this can be problematic.
+ The only known solution at this point is to turn off checkpointing by setting
+ the 
+\family typewriter
+checkpointEvery
+\family default
+ parameter to 0.
+ The VTK files do not suffer from this problem.
+\end_layout
+
 \begin_layout Section
 Output and Visualization
 \end_layout
@@ -2228,15 +2337,15 @@
 maxZ
 \family default
 ).
- Finally, vary the tolerance for each nonlinear iteration (
+ Finally, vary the tolerance for each linear and nonlinear iteration (
 \family typewriter
-tolerance
+linearTolerance
 \family default
- in the 
+ and 
 \family typewriter
-uzawa
+nonlinearTolerance
 \family default
- component).
+).
 \end_layout
 
 \begin_layout Standard
@@ -3442,6 +3551,7 @@
 status open
 
 \begin_layout Standard
+\align center
 \begin_inset Graphics
 	filename images/Paraview_viscous_inflow.png
 	lyxscale 75
@@ -3475,6 +3585,259 @@
 \end_layout
 
 \begin_layout Section
+Viscous Material with Inflow/Outflow and Fixed Internal Degrees of Freedom
+\end_layout
+
+\begin_layout Standard
+Some problems do not lend themselves to simple, rectangular domains.
+ In these cases, it may be convenient to have the simulation cover a regular
+ domain but then fix some internal degrees of freedom.
+ This example modifies the inflow/outflow example in Section 
+\begin_inset LatexCommand ref
+reference "sec:Viscous-In-Outflow"
+
+\end_inset
+
+ to force the flow to be straight in from the side as in Figure 
+\begin_inset LatexCommand ref
+reference "fig:Inflow/Outflow-Boundary-with"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+	filename images/inflow_fixed.eps
+	width 80col%
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Inflow/Outflow-Boundary-with"
+
+\end_inset
+
+Inflow/Outflow Boundary with Fixed Internal Degrees of Freedom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This could be the first step in constructing a pipe that injects flow into
+ the bulk material.
+ To finish the pipe, you need to create a region around the inflow, perhaps
+ of a different material, that has zero velocity.
+ In this example, we will only do this first step.
+ Creating the entire pipe is left as an exercise to the reader.
+\end_layout
+
+\begin_layout Enumerate
+Copy 
+\family typewriter
+my_viscous_inflow.xml
+\family default
+ to 
+\family typewriter
+my_viscous_fixed.xml
+\family default
+.
+\end_layout
+
+\begin_layout Enumerate
+Create a shape for the fixed region
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct name="fixedShape">
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="Type">Box</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="startX">minX</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="endX">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="startY">StepFunctionProduct3Start</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="endY">StepFunctionProduct3End</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="startZ">minZ</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="endZ">maxZ</param> 
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Add a ShapeVC to the list of velocity conditions
+\end_layout
+
+\begin_deeper
+\begin_layout LyX-Code
+<struct>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="type">ShapeVC</param>
+\end_layout
+
+\begin_layout LyX-Code
+  <param name="Shape">fixedShape</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">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+      <param name="value">StepFunctionProduct3Value</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">double</param>
+\end_layout
+
+\begin_layout LyX-Code
+      <param name="value">0.0</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 Standard
+A worked example is in 
+\family typewriter
+input/cookbook/viscous_fixed.xml
+\family default
+.
+ A visualization of the strain rate invariant and velocity (see Section
+ 
+\begin_inset LatexCommand ref
+reference "sub:Visualization-with-ParaView"
+
+\end_inset
+
+) is shown in Figure 
+\begin_inset LatexCommand ref
+reference "fig:Strain-fixed"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+	filename images/Paraview_viscous_fixed.png
+	scale 45
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Strain-fixed"
+
+\end_inset
+
+Strain rate invariant and velocities with inflow/outflow and fixed internal
+ degrees of freedom
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
 Viscous Material in Extension with Normal Stress Boundaries
 \end_layout
 
@@ -4546,10 +4909,6 @@
 \end_layout
 
 \begin_layout LyX-Code
-  <param name="minimumYieldStress">0.00001</param>
-\end_layout
-
-\begin_layout LyX-Code
 </struct>
 \end_layout
 
@@ -5450,6 +5809,104 @@
 \end_layout
 
 \begin_layout Chapter
+Geologic Example
+\end_layout
+
+\begin_layout Standard
+The previous chapter gave examples on how to make simple problems with simple
+ parameters (e.g.
+ length=1, viscosity=1).
+ Scaling these input parameters to realistic values (e.g.
+ length=1000km, viscosity=
+\begin_inset Formula $10^{26}$
+\end_inset
+
+) should be as easy as changing the various parameters to the right number.
+ In practice, it can be difficult to get right, because you may have to
+ change many different parameters at once to ensure stability.
+ To make that transition easier, there is are sample input files in 
+\family typewriter
+input/examples/tibet.xml
+\family default
+ and 
+\family typewriter
+input/examples/tibet3D.xml
+\family default
+.
+ These are the input files used to create the cover images.
+ The first file simulates a tibetan scale plateau under extension in 2D.
+ A schematic of the simulation is shown in Figure 
+\begin_inset LatexCommand ref
+reference "fig:Schematic-of-extension"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+	filename images/tibet_setup.eps
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Schematic-of-extension"
+
+\end_inset
+
+Schematic of extension example
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The 3D input file layers a uniform thickness of crust onto a mantle, but
+ then imports a realistic topography from a data file.
+ At the moment, this location is hard coded in 
+\family typewriter
+src/StGermain/Discretisation/Mesh/src/SurfaceAdaptor.c
+\family default
+.
+ It needs a data file 
+\family typewriter
+ascii_topo
+\family default
+.
+ This file is very large, so it is not distributed with Gale.
+ You may download it from 
+\begin_inset LatexCommand url
+target "http://geodynamics.org/~walter/ascii_topo"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Chapter
 Modifying Gale
 \begin_inset LatexCommand label
 name "cha:Modifying-Gale"
@@ -11263,6 +11720,15 @@
 
  When the material is yielding, the viscosity is modified so that the stress
  on the particle is the yield stress.
+ Note that 
+\family typewriter
+minimumYieldStress
+\family default
+ is interpreted differently.
+ If it is zero (the default), then actual minimum yield stress will be the
+ effective cohesion.
+ This is because there tends to be numerical problems when using a very
+ small minimum yield stress under tension.
 \newline
 
 \end_layout
@@ -11387,7 +11853,7 @@
 \begin_inset Text
 
 \begin_layout Standard
-0
+0 (see above)
 \end_layout
 
 \end_inset
@@ -13583,7 +14049,12 @@
 \end_layout
 
 \begin_layout Section
+\begin_inset LatexCommand label
+name "sec:.dat-ASCII-Files"
 
+\end_inset
+
+
 \family typewriter
 .dat
 \family default
@@ -13907,63 +14378,377 @@
 \end_layout
 
 \begin_layout Standard
-CIG has worked with Susanne Buiter at NGU to improve the benchmak specifications.
- Gale has been tested with relaxation of topography, extension, shortening,
- and subduction models.
+Gale has been tested against a number of different benchmarks.
 \end_layout
 
 \begin_layout Section
+\begin_inset LatexCommand label
+name "sec:Circular-Inclusion"
+
+\end_inset
+
 Circular Inclusion
 \end_layout
 
 \begin_layout Standard
-To check the results yourself, run the accompanying input file with 3 different
- resolutions:
+\begin_inset LatexCommand cite
+key "Clast"
+
+\end_inset
+
+ derived a simple analytic solution for the pressure and velocity fields
+ for a circular inclusion under simple shear.
+ The file 
+\family typewriter
+input/benchmarks/circular_inclusion/README
+\family default
+ has instructions on how to run this benchmark.
+ Figure xxx plots the strain rate and velocities of a medium resolution
+ run.
+ Because of the symmetry of the problem, we only have to solve over a quarter
+ of the domain.
 \end_layout
 
-\begin_layout LyX-Code
-Gale spherical_inclusion.xml --outputPath=64 -pc_type lu -ksp_type preonly
+\begin_layout Standard
+Figure xxx plots the error in the pressure along the x axis as you change
+ resolution and distance to the boundary.
+ As you increase resolution and move the boundary away, the numerical solution
+ converges to the analytic solution.
 \end_layout
 
-\begin_layout LyX-Code
-Gale spherical_inclusion.xml --elementResI=128 --elementResJ=128 --outputPath=128
+\begin_layout Section
+\begin_inset LatexCommand label
+name "sec:Falling-Sphere"
+
+\end_inset
+
+Falling Sphere
+\end_layout
+
+\begin_layout Standard
+This benchmark simulates a rigid sphere falling through a viscous medium.
+ The file 
+\family typewriter
+input/benchmarks/falling_sphere/README
+\family default
+ has instructions on running this benchmark.
+ The analytic solution for the drag on a sphere is
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+F=6\pi\eta Ru,\]
+
+\end_inset
+
+ where 
+\begin_inset Formula $\eta$
+\end_inset
+
+ is the viscosity of the medium, 
+\begin_inset Formula $R$
+\end_inset
+
+ is the radius of the sphere, and 
+\begin_inset Formula $u$
+\end_inset
+
+ is the velocity of the sphere.
+ Conversely, the buoyancy force is
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+F=\frac{4}{3}\pi R^{3}g\delta\rho,\]
+
+\end_inset
+
+where 
+\begin_inset Formula $g$
+\end_inset
+
+ is the gravitational constant and 
+\begin_inset Formula $\delta\rho$
+\end_inset
+
+ is the density difference between the sphere and the medium.
+ Balancing these two forces and solving for the velocity gives
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+u=\frac{2}{9}R^{2}g\delta\rho/\eta.\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Setting 
+\begin_inset Formula $g=1$
+\end_inset
+
+, 
+\begin_inset Formula $R=1$
+\end_inset
+
+, 
+\begin_inset Formula $\delta\rho=0.01$
+\end_inset
+
+, and 
+\begin_inset Formula $\eta=1$
+\end_inset
+
+ gives a velocity of 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+u=0.00222.\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In our case, we simulate a rigid sphere with a high viscosity sphere.
+ This allows some internal circulation within the sphere, and so the expression
+ for the velocity becomes 
+\begin_inset LatexCommand cite
+key "Intro to Fluid Dynamics"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+u=\frac{1}{3}\frac{R^{2}g\delta\rho}{\eta}\frac{\eta+\eta'}{\eta+\frac{3}{2}\eta'},\]
+
+\end_inset
+
+ where 
+\begin_inset Formula $\eta'$
+\end_inset
+
+is the viscosity of the sphere.
+ For our case, the background medium's viscosity is 1 and the sphere's viscosity
+ is 100, so the correction is about 1%.
+ This turns out to be smaller than other effects for the cases we ran.
+\end_layout
+
+\begin_layout Standard
+The analytic solution also assumes infinitely small Reynolds number.
+ Expanding the drag in terms of the Reynolds number gives 
+\begin_inset LatexCommand cite
+key "Landau & Lifschitz"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+F=6\pi\eta Ru\left(1+\frac{3uR}{8\eta}\right)\]
+
+\end_inset
+
+ which gives a correction of order 0.1%.
+ If we had made 
+\begin_inset Formula $\delta\rho$
+\end_inset
+
+ or 
+\begin_inset Formula $g$
+\end_inset
+
+ larger, then this would have become more important.
+\end_layout
+
+\begin_layout Standard
+Finally, the solution assumes that the boundaries are inifinitely far away.
+ So we vary the distance to the boundary to gauge exactly how much the boundarie
+s affect the solution.
+\end_layout
+
+\begin_layout Section
+\begin_inset LatexCommand label
+name "sec:Falling-Cylinder"
+
+\end_inset
+
+Falling Cylinder
+\end_layout
+
+\begin_layout Standard
+This benchmark is very similar to the falling sphere case and uses the same
+ input file.
+ We can write down an expression for the drag 
+\begin_inset LatexCommand cite
+key "Landau & Lifschitz"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+F=\frac{4\pi\eta u}{\log\left(3.70\eta/uR\right)},\]
+
+\end_inset
+
  
-\newline
--pc_type lu -ksp_type preonly
 \end_layout
 
-\begin_layout LyX-Code
-Gale spherical_inclusion.xml --elementResI=256 --elementResJ=256 --outputPath=256
+\begin_layout Standard
+and the buoyancy force
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+F=\pi R^{2}g\delta\rho.\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For the same parameters as above, a nonlinear solve gives a velocity of
  
-\newline
--pc_type lu -ksp_type preonly
 \end_layout
 
 \begin_layout Standard
-The last run will require about 800MB of memory and take about 30 minutes
- on a recent-era machine.
- Then run ParaView and load in the state file
+\begin_inset Formula \[
+u=0.0140.\]
+
+\end_inset
+
+
 \end_layout
 
-\begin_layout LyX-Code
-spherical_inclusion.pvsm
+\begin_layout Standard
+This solution is subject to the same caveats regarding the finite viscosity
+ of the cylinder, finite Reynolds number, and boundary effects.
+ It turns out, though, that the boundary effects are much stronger in this
+ case than in 3D.
+ As the Figure xxx shows, the boundary has to be moved extremely far away
+ to see convergence to the analytic solution.
 \end_layout
 
+\begin_layout Section
+Relaxation of Topography
+\end_layout
+
 \begin_layout Standard
-That will give you a picture like Figure 
+Given an infinitely deep purely viscous medium with an infinitesimal initial
+ sinusoidal height profile, the topography will decay exponentially with
+ the timescale 
+\begin_inset LatexCommand cite
+key "Folds"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+t_{r}=\frac{4\pi\eta}{gL},\]
+
+\end_inset
+
+ where 
+\begin_inset Formula $\eta$
+\end_inset
+
+ is the viscosity, 
+\begin_inset Formula $g$
+\end_inset
+
+ is the gravitational constant, and 
+\begin_inset Formula $L$
+\end_inset
+
+ is the wavelength of the initial sinusoid.
+ 
+\end_layout
+
+\begin_layout Standard
+In our case, we simulate a medium with finite depth and finite height.
+ The internal fields decay exponentially with depth with a length scale
+ of 
+\begin_inset Formula $L/2\pi.$
+\end_inset
+
+ The error in the solution due to a finite height is of order 
+\begin_inset Formula $\left(2\pi A/L\right)^{2},$
+\end_inset
+
+ where 
+\begin_inset Formula $A$
+\end_inset
+
+ is the amplitude of the sinusoid.
+ We use 
+\begin_inset Formula $L=1$
+\end_inset
+
+ and 
+\begin_inset Formula $A=0.01,$
+\end_inset
+
+ giving errors of order 0.2% and 0.4%.
+\end_layout
+
+\begin_layout Standard
+The file 
+\family typewriter
+input/benchmarks/sinusoid/README
+\family default
+ explains how to run this benchmark.
+ Figure 
 \begin_inset LatexCommand ref
-reference "fig:Circular Inclusion error"
+reference "fig:Strain-topo"
 
 \end_inset
 
+ shows the results of a low resolution run.
+ Even this run is not that small (128x256), because we need fairly high
+ resolution to be able to accurately resolve the small (1%) height difference.
+ Also note that we use symmetry to only simulate half of the wavelength.
+ 
+\end_layout
+
+\begin_layout Standard
+Running the code with multiple resolutions and measuring the error in the
+ height in the trough gives Figure 
+\begin_inset LatexCommand ref
+reference "fig:topo-error"
+
+\end_inset
+
 .
- The high resolution error (blue) is less than the medium resolution error
- (green), which is less than the low resolution error (red).
+ Scaling the high resolution error by 4 and the medium resolution by 2 gives
+ Figure 
+\begin_inset LatexCommand ref
+reference "fig:scaled-topo-error"
+
+\end_inset
+
+.
+ The error decreases linearly with increasing resolution, giving us confidence
+ in our ability to accurately track topography.
 \end_layout
 
 \begin_layout Standard
 \begin_inset Float figure
-placement H
 wide false
 sideways false
 status open
@@ -13971,39 +14756,99 @@
 \begin_layout Standard
 \align center
 \begin_inset Graphics
-	filename images/circular_inclusion_error.png
-	width 80col%
-	keepAspectRatio
+	filename images/Paraview_topography.png
 
 \end_inset
 
 
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Strain-topo"
+
+\end_inset
+
+Strain rate and velocities for a sinusoidal topography relaxing under gravity
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+	filename images/topo_error.eps
+
+\end_inset
+
+
 \begin_inset Caption
 
 \begin_layout Standard
 \begin_inset LatexCommand label
-name "fig:Circular Inclusion error"
+name "fig:topo-error"
 
 \end_inset
 
-Numerical error for the circular inclusion benchmark around the interface
- between the low and high viscosity regision.
- Blue is high resolution (256 
-\begin_inset Formula $\times$
+Error in the height at the trough
+\end_layout
+
 \end_inset
 
- 256), green is medium resolution (128 
-\begin_inset Formula $\times$
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
 \end_inset
 
- 128), and red is low resolution (64 
-\begin_inset Formula $\times$
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+	filename images/topo_scaled_error.eps
+
 \end_inset
 
- 64).
+
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:scaled-topo-error"
+
+\end_inset
+
+Error in the height at the trough scaled with resolution
 \end_layout
 
 \end_inset
@@ -14016,12 +14861,96 @@
 
 \end_layout
 
+\begin_layout Section
+\begin_inset LatexCommand label
+name "sec:Geomod-2004"
+
+\end_inset
+
+Geomod 2004
+\end_layout
+
 \begin_layout Standard
-Far away from the hole, the error becomes dominated by factors other than
- finite resolution (e.g., finite distance to the boundary and non-zero tolerance
- when solving the Stokes flow).
+Two benchmarks were set up to validate numerical codes against analogue
+ sandbox experiments 
+\begin_inset LatexCommand cite
+key "Geomod 2004"
+
+\end_inset
+
+.
+ One benchmark models extension, and the other models shortening.
+ At this time, Gale has partially implemented the extension benchmark.
+ The input file is in 
+\family typewriter
+input/benchmarks/extension.xml
+\family default
+.
+ The result of running the benchmark, using a direct solver in parallel,
+ is shown in Figure 
+\begin_inset LatexCommand ref
+reference "fig:Strain-Geomod"
+
+\end_inset
+
+.
 \end_layout
 
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+	filename images/strainrate_1cm.png
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Strain-Geomod"
+
+\end_inset
+
+Strain rate invariant after 1cm of extension
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+While it is difficult to perform exact comparisons, Gale does reproduce
+ the multiple interlaced faults seen in both numerical and analogue experiments.
+ However, the faults that Gale produces are not straight.
+ This is probably because the viscosity we used for sand was on the low
+ end (
+\begin_inset Formula $5\cdot10^{7}$
+\end_inset
+
+).
+ Using higher viscosities caused the solver to stop converging.
+\end_layout
+
 \begin_layout Chapter
 License 
 \end_layout
@@ -14777,5 +15706,93 @@
 , 11, 063-11, 082 
 \end_layout
 
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+label "8"
+key "Clast"
+
+\end_inset
+
+Schmid, D.
+ W., and Y.
+ Y.
+ Podladchikov (2003), Analytical solutions for deformable elliptical inclusions
+ in general shear, 
+\shape italic
+Geophys.
+ J.
+ Int.
+\shape default
+, 
+\shape italic
+155
+\shape default
+, 269-288
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+label "9"
+key "Intro to Fluid Dynamics"
+
+\end_inset
+
+ Batchelor, G.
+ K (1967), An Introduction to Fluid Dynamics, Cambridge University Press,
+ p236
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+label "10"
+key "Landau & Lifschitz"
+
+\end_inset
+
+ Landau, L.
+ D, and E.
+ M.
+ Lifshitz (1987), Fluid Mechanics, Pergamon Press, p61-62
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+label "11"
+key "Folds"
+
+\end_inset
+
+ Johnson, A.
+ M., and R.
+ C.
+ Fletcher, Folding of Viscous Layers (1994), Columbia University Press,
+ p19
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+label "12"
+key "Geomod 2004"
+
+\end_inset
+
+Analogue and Numerical Modelling of Crustal-Scale Processes , Buiter, S.J.H.
+ and Schreurs, G.
+ (eds), Geological Society, London, Special Publications, 253 : Schreurs,
+ G., Buiter, S.J.H., Boutelier, D., Corti, G., Costa, E., Cruden, A., Daniel, J.-M.,
+ Hoth, S., Koyi, H., Kukowski, N., Lohrmann, J., Ravaglia, A., Schlische, R.W.,
+ Withjack, M.O., Yamada, Y., Cavozzi, C., DelVentisette, C., Elder Brady, J.,
+ Hoffmann-Rothe, A., Mengus, J.-M., Montanari, D., and Nilforoushan, F., 2006,
+ Analogue benchmarks of shortening and extension experiments, p.
+ 1-27 * Susanne J.H.
+ Buiter, Andrey Yu.
+ Babeyko, Susan Ellis, Taras V.
+ Gerya, Boris J.P.
+ Kaus, Antje Kellner, Guido Schreurs, and Yasuhiro Yamada, 2006, The numerical
+ sandbox: comparison of model results for a shortening and an extension
+ experiment, p.
+ 29-64 
+\end_layout
+
 \end_body
 \end_document

Added: long/3D/Gale/trunk/documentation/images/Paraview_topography.png
===================================================================
(Binary files differ)


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___________________________________________________________________
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Added: long/3D/Gale/trunk/documentation/images/Paraview_viscous_fixed.png
===================================================================
(Binary files differ)


Property changes on: long/3D/Gale/trunk/documentation/images/Paraview_viscous_fixed.png
___________________________________________________________________
Name: svn:mime-type
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Added: long/3D/Gale/trunk/documentation/images/inflow_fixed.eps
===================================================================
--- long/3D/Gale/trunk/documentation/images/inflow_fixed.eps	                        (rev 0)
+++ long/3D/Gale/trunk/documentation/images/inflow_fixed.eps	2008-03-10 18:45:34 UTC (rev 11392)
@@ -0,0 +1,583 @@
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Added: long/3D/Gale/trunk/documentation/images/inflow_fixed.fig
===================================================================
--- long/3D/Gale/trunk/documentation/images/inflow_fixed.fig	                        (rev 0)
+++ long/3D/Gale/trunk/documentation/images/inflow_fixed.fig	2008-03-10 18:45:34 UTC (rev 11392)
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Added: long/3D/Gale/trunk/documentation/images/tibet_setup.eps
===================================================================
--- long/3D/Gale/trunk/documentation/images/tibet_setup.eps	                        (rev 0)
+++ long/3D/Gale/trunk/documentation/images/tibet_setup.eps	2008-03-10 18:45:34 UTC (rev 11392)
@@ -0,0 +1,529 @@
+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: tibet_setup.fig
+%%Creator: fig2dev Version 3.2 Patchlevel 5
+%%CreationDate: Mon Mar 10 11:16:12 2008
+%%For: boo at earth (Walter Landry,,,)
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Added: long/3D/Gale/trunk/documentation/images/tibet_setup.fig
===================================================================
--- long/3D/Gale/trunk/documentation/images/tibet_setup.fig	                        (rev 0)
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===================================================================
--- long/3D/Gale/trunk/documentation/images/topo_scaled_error.eps	                        (rev 0)
+++ long/3D/Gale/trunk/documentation/images/topo_scaled_error.eps	2008-03-10 18:45:34 UTC (rev 11392)
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