[cig-commits] r15862 - in doc/geodynamics.org/benchmarks/trunk: . geodyn long mc mc/2d-cartesian mc/3d-spherical short
luis at geodynamics.org
luis at geodynamics.org
Wed Oct 21 15:34:15 PDT 2009
Author: luis
Date: 2009-10-21 15:34:13 -0700 (Wed, 21 Oct 2009)
New Revision: 15862
Modified:
doc/geodynamics.org/benchmarks/trunk/geodyn/index.html
doc/geodynamics.org/benchmarks/trunk/index.html
doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.html
doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.rst
doc/geodynamics.org/benchmarks/trunk/long/divergence.html
doc/geodynamics.org/benchmarks/trunk/long/divergence.rst
doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html
doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst
doc/geodynamics.org/benchmarks/trunk/long/geomod2004.html
doc/geodynamics.org/benchmarks/trunk/long/geomod2004.rst
doc/geodynamics.org/benchmarks/trunk/long/geomod2008.html
doc/geodynamics.org/benchmarks/trunk/long/geomod2008.rst
doc/geodynamics.org/benchmarks/trunk/long/index.html
doc/geodynamics.org/benchmarks/trunk/long/index.rst
doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html
doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/index.rst
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.html
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.rst
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.html
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.rst
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.html
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.rst
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.html
doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.rst
doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.html
doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.rst
doc/geodynamics.org/benchmarks/trunk/mc/index.html
doc/geodynamics.org/benchmarks/trunk/mc/index.rst
doc/geodynamics.org/benchmarks/trunk/short/index.html
doc/geodynamics.org/benchmarks/trunk/short/index.rst
Log:
Imported changes from website (2009-10-21)
Modified: doc/geodynamics.org/benchmarks/trunk/geodyn/index.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/geodyn/index.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/geodyn/index.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -14,30 +14,30 @@
<div class="section" id="historical-benchmark-cases">
<h1>Historical Benchmark Cases</h1>
-<p>Historically, there are two cases defined in the benchmark study published
-in the 2001 paper by Christensen et al. [6]. Case 0 is a benchmark of rotating
+<p>There are two cases defined in the benchmark study published
+in the 2001 paper by Christensen et al. Case 0 is a benchmark of rotating
non-magnetic convection. Case 1 is a dynamo with an insulating inner core
co-rotating with the outer boundary. The regions outside the fluid shell are
electrical insulators and the magnetic field on the boundaries matches with
appropriate potential fields in the exterior that imply no external sources
of the field.</p>
-<p>In both cases the Ekman number is [;E = 10^{3};] and the Prandtl number is
+<p>In both cases the Ekman number is [;E = 10^{-3};] and the Prandtl number is
[;Pr = 1;]. The Rayleigh number is set to [;Ra = 100000;]. Note that the
definition of the Rayleigh number differs from the one in the published
-cases [6] by a factor of Ekman number, i.e., [;Ra=\frac{Ra}{E};]. The
+cases by a factor of Ekman number [;E;], i.e., [;Ra=\frac{Ra}{E};]. The
magnetic Prandtl number is zero in the non-magnetic convection case 0, and
is [;Pm = 5;] in case 1. The spherical harmonic expansion is truncated at
-degree [;\ell_{max}=32;] and a four-fold symmetry is assumed in the
+degree [;lmax=32;] and a four-fold symmetry is assumed in the
longitudinal direction (the file <tt class="docutils literal"><span class="pre">param.f</span></tt> should be linked to
<tt class="docutils literal"><span class="pre">param32s4.f</span></tt> when you compile MAG). The input parameter files are
<tt class="docutils literal"><span class="pre">par.bench0</span></tt> for case 0, and <tt class="docutils literal"><span class="pre">par.bench1</span></tt> for case 1; both files
reside in the <tt class="docutils literal"><span class="pre">~/src</span></tt> directory.</p>
-<p>The output files of the benchmark cases are stored n the directory
-<tt class="docutils literal"><span class="pre">~/bench-data/data_bench0</span></tt> and <tt class="docutils literal"><span class="pre">~/bench-data/data-bench1</span></tt> respectively.
+<p>The output files of the benchmark cases are stored in the directory
+<tt class="docutils literal"><span class="pre">~/bench-data/data_bench0</span></tt> and <tt class="docutils literal"><span class="pre">~/bench-data/data_bench1</span></tt> respectively.
In the following table we see the solutions from MAG agree with the
benchmark suggested value with a small margin of difference. In both case 0
and case 1, the values listed were obtained with low resolution and a
-relatively short run of MAG</p>
+relatively short run of MAG.</p>
<table border="1" class="docutils">
<colgroup>
<col width="20%" />
@@ -134,8 +134,7 @@
<div align="center" class="figure">
<img alt="pole plot" src="images/g7revR.png" />
<p class="caption"><span class="target" id="figure-p2">Figure P2</span>:
-Magnetic field pole plot, at the end
-of the second field reversal</p>
+Magnetic field pole plot, at the end of the second field reversal.</p>
</div>
<!-- plus or minus sign -->
<!-- http://www.fileformat.info/info/unicode/char/00b1/index.htm -->
Modified: doc/geodynamics.org/benchmarks/trunk/index.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/index.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/index.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,15 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Software Verification</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="software-verification">
-<h1 class="title">Software Verification</h1>
-<h2 class="subtitle" id="benchmark-efforts-by-working-group">Benchmark Efforts by Working Group</h2>
+<div class="document">
+
<ul class="simple">
<li><a class="reference external" href="geodyn">Geodynamo</a></li>
<li><a class="reference external" href="long">Long-Term Tectonics</a></li>
Modified: doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Circular Inclusion</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="circular-inclusion">
-<h1 class="title">Circular Inclusion</h1>
+<div class="document">
+
<p>Schmid and Podladchikov [Clast] derived a simple analytic solution for
the pressure and velocity fields for a circular inclusion under simple
shear as in <a class="reference internal" href="#figure-1">Figure 1</a>.</p>
@@ -54,15 +54,15 @@
<p><a class="reference internal" href="#figure-2">Figure 2</a> plots the error in the pressure along the line [;y=x/2;]
for different resolutions. Inside the inclusion near the surface,
the pressure is consistently wrong. The pressure does not converge
-with higher resolution, giving us a clue that the default
-numerical scheme is not accurate.</p>
+with higher resolution, giving us a clue that the
+numerical scheme is not completely accurate.</p>
<!-- fig:Pressure-Inclusion -->
<div align="center" class="figure">
<img alt="Pressure Field" src="images/inclusion_r8_p.png" style="width: 600px;" />
<p class="caption"><span class="target" id="figure-2">Figure 2</span>:
Pressure along the line [;y=x/2;] for resolutions of
128 × 128 (blue), 256 × 256 (red),
-and 512 × 512 (black). The inclusion has radius
+and 512 × 512 (black). The inclusion has a radius
[;r_i=0.1;]. Note that the pressure should be zero
inside the inclusion, but the numerical solutions
consistently underestimate the pressure.</p>
@@ -85,7 +85,7 @@
Error in the pressure outside the inclusion along
the line [;y=x/2;] for resolutions of 128 × 128 (blue),
256 × 256 (red), and 512 × 512 (black).
-The inclusion has radius [;r_i=0.1;].</p>
+The inclusion has a radius [;r_i=0.1;].</p>
</div>
<!-- fig:Scaled-pressure-error -->
<div align="center" class="figure">
Modified: doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/circular-inclusion.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,6 +1,3 @@
-Circular Inclusion
-==================
-
Schmid and Podladchikov [Clast] derived a simple analytic solution for
the pressure and velocity fields for a circular inclusion under simple
shear as in `Figure 1`_.
@@ -52,8 +49,8 @@
`Figure 2`_ plots the error in the pressure along the line [;y=x/2;]
for different resolutions. Inside the inclusion near the surface,
the pressure is consistently wrong. The pressure does not converge
-with higher resolution, giving us a clue that the default
-numerical scheme is not accurate.
+with higher resolution, giving us a clue that the
+numerical scheme is not completely accurate.
.. fig:Pressure-Inclusion
.. figure:: images/inclusion_r8_p.png
@@ -64,7 +61,7 @@
_`Figure 2`:
Pressure along the line [;y=x/2;] for resolutions of
128 |times| 128 (blue), 256 |times| 256 (red),
- and 512 |times| 512 (black). The inclusion has radius
+ and 512 |times| 512 (black). The inclusion has a radius
[;r_i=0.1;]. Note that the pressure should be zero
inside the inclusion, but the numerical solutions
consistently underestimate the pressure.
@@ -92,7 +89,7 @@
Error in the pressure outside the inclusion along
the line [;y=x/2;] for resolutions of 128 |times| 128 (blue),
256 |times| 256 (red), and 512 |times| 512 (black).
- The inclusion has radius [;r_i=0.1;].
+ The inclusion has a radius [;r_i=0.1;].
.. fig:Scaled-pressure-error
Modified: doc/geodynamics.org/benchmarks/trunk/long/divergence.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/divergence.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/divergence.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,15 +4,15 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Divergence</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="divergence">
-<h1 class="title">Divergence</h1>
+<div class="document">
-<p>This benchmark tests the implementation of the divergence term in the
+
+<p>This benchmark tests the implementation of the divergence term in
equation [eq:divergence]. In 2D, a constant divergence is applied to a
square domain, and the velocity on the corners is set to enforce a
spreading from the center of the square. <a class="reference internal" href="#figure-1">Figure 1</a> shows the velocity
@@ -20,16 +20,16 @@
divergence [;d;], the analytic solution for this setup is</p>
<blockquote>
[;\begin{align*}
-v_x &= x \cdot d/2, \\
+v_x &= x \cdot d/2 \\
v_y &= y \cdot d/2
-\end{align*} ;]</blockquote>
+\end{align*}. ;]</blockquote>
<p>In 3D, the analytic solution is</p>
<blockquote>
[;\begin{align*}
-v_x &= x \cdot d/3, \\
-v_y &= y \cdot d/3, \\
+v_x &= x \cdot d/3 \\
+v_y &= y \cdot d/3 \\
v_z &= z \cdot d/3
-\end{align*};]</blockquote>
+\end{align*}.;]</blockquote>
<p>In both cases, the strain rate invariant equals [;\sqrt{d/2};].
As shown in <a class="reference internal" href="#figure-2">Figure 2</a>, the main source of error in 2D comes
from inaccuracies in the solver. <a class="reference internal" href="#figure-3">Figure 3</a> paints a different
Modified: doc/geodynamics.org/benchmarks/trunk/long/divergence.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/divergence.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/divergence.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,4 @@
-
-Divergence
-==========
-
-This benchmark tests the implementation of the divergence term in the
+This benchmark tests the implementation of the divergence term in
equation [eq:divergence]. In 2D, a constant divergence is applied to a
square domain, and the velocity on the corners is set to enforce a
spreading from the center of the square. `Figure 1`_ shows the velocity
@@ -10,17 +6,17 @@
divergence [;d;], the analytic solution for this setup is
[;\\begin{align*}
- v_x &= x \\cdot d/2, \\\\
+ v_x &= x \\cdot d/2 \\\\
v_y &= y \\cdot d/2
- \\end{align*} ;]
+ \\end{align*}. ;]
In 3D, the analytic solution is
[;\\begin{align*}
- v_x &= x \\cdot d/3, \\\\
- v_y &= y \\cdot d/3, \\\\
+ v_x &= x \\cdot d/3 \\\\
+ v_y &= y \\cdot d/3 \\\\
v_z &= z \\cdot d/3
- \\end{align*};]
+ \\end{align*}.;]
In both cases, the strain rate invariant equals [;\\sqrt{d/2};].
As shown in `Figure 2`_, the main source of error in 2D comes
Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Drucker-Prager</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="drucker-prager">
-<h1 class="title">Drucker-Prager</h1>
+<div class="document">
+
<div class="section" id="analytic-treatment">
<h1>Analytic Treatment</h1>
<p>For the Drucker-Prager rehology in 2D, we can write the
@@ -65,7 +65,7 @@
our Drucker-Prager implementation gives the correct results.</p>
<!-- fig:Mohr-Coulomb-sri -->
<div align="center" class="figure">
-<img alt="images/Mohr_coulomb_resolutions.png" src="images/Mohr_coulomb_resolutions.png" style="width: 400px;" />
+<img alt="images/Mohr_Coulomb_resolutions.png" src="images/Mohr_Coulomb_resolutions.png" style="width: 400px;" />
<p class="caption"><span class="target" id="figure-2">Figure 2</span>:
Strain rate invariant for the shortening experiment where
[;\varphi=45^{\circ};] with three different resolutions:
Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,7 +1,3 @@
-
-Drucker-Prager
-==============
-
Analytic Treatment
------------------
@@ -66,7 +62,7 @@
.. fig:Mohr-Coulomb-sri
-.. figure:: images/Mohr_coulomb_resolutions.png
+.. figure:: images/Mohr_Coulomb_resolutions.png
:align: center
:width: 400
Modified: doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Falling Sphere</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="falling-sphere">
-<h1 class="title">Falling Sphere</h1>
+<div class="document">
+
<p>This benchmark simulates a rigid sphere falling through
a cylinder filled with a viscous medium as in <a class="reference internal" href="#figure-1">Figure 1</a>.</p>
<!-- fig:Sphere-Cylinder -->
@@ -25,7 +25,7 @@
solution for the drag on a sphere is</p>
<blockquote>
[;F=6\pi\eta r u,;]</blockquote>
-<p>where [;eta;] is the viscosity of the medium, [;r;] is the radius of the
+<p>where [;\eta;] is the viscosity of the medium, [;r;] is the radius of the
sphere, and [;u;] is the velocity of the sphere. Conversely, the
buoyancy force is</p>
<blockquote>
@@ -35,7 +35,7 @@
two forces and solving for the velocity gives</p>
<blockquote>
[;u = \frac{2}{9}{r^2}g\delta\rho / \eta.;]</blockquote>
-<p>Seetting [;g=1;], [;r=1;], [;\delta\rho=0.01;], and [;\eta=1;]
+<p>Setting [;g=1;], [;r=1;], [;\delta\rho=0.01;], and [;\eta=1;]
gives a velocity of</p>
<blockquote>
[;u=0.00222.;]</blockquote>
@@ -44,22 +44,38 @@
expression for the velocity becomes [Landau & Lifschitz],</p>
<blockquote>
[;u = \frac{1}{3}\frac{r^2{g}\delta\rho}{\eta}\frac{\eta+\eta'}{\eta+\frac{3}{2}\eta'},;]</blockquote>
-<p>where [;\eta';] is the viscosity of the sphere. Four our case, the
+<p>where [;\eta';] 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.</p>
-<p>when the boundaries are not infinitely far away, we can expand the
+<p>When the boundaries are not infinitely far away, we can expand the
solution in terms of the ratio of the radius of the sphere ([;r;]) to the
radius of the cylinder ([;R;]). One solution by Habermann [Stokes Sphere]
gives a drag force of</p>
<blockquote>
-[;F_H=6\pi\eta{ru}\frac{1-0.75857\left(\frac{r}{R}\right)^5}{1+f_H\left(\frac{r}{R}\right)},;]</blockquote>
+[;F_H=6\pi\eta{ru}\frac{1-0.75857\cdot\left(\frac{r}{R}\right)^5}{1+f_H\left(\frac{r}{R}\right)},;]</blockquote>
<p>where</p>
<blockquote>
-[;f_H\left(\frac{r}{R}\right)=-2.1050(r/R)+2.0865(r/R)^3-1.7068(r/R)^5+0.72603(r/R)^6.;]</blockquote>
+[;f_H\left(\frac{r}{R}\right) =
+-2.1050(r/R) + 2.0865(r/R)^3
+-1.7068(r/R)^5+0.72603(r/R)^6.;]</blockquote>
<p>For our case with [;r=1;], [;R=4;], this gives a velocity of</p>
<blockquote>
-[;u=1.122747319\cdot{10^{-3}},;]</blockquote>
+[;u=1.122747319\cdot{10^{-3}}.;]</blockquote>
+<p>The walls reduce the speed by about a factor of two.</p>
+<p>Another solution by Faxen [Lindgren] gives a drag force of</p>
+<blockquote>
+[;F_F=6\pi\eta{ru}/(1+f_F(r/R)),;]</blockquote>
+<p>where</p>
+<blockquote>
+[;\begin{eqnarray*}
+f_f\left(r/R\right)=&-&2.10444(r/R)+2.08877
+(r/R)^3-0.94813(r/R)^5 \\
+&-&1.372(r/R)^6+3.87(r/R)^8-4.19(r/R)^{10}.
+\end{eqnarray*};]</blockquote>
+<p>For our case, this gives a speed of</p>
+<blockquote>
+[;u=1.12293603939\cdot{10^{-3}},;]</blockquote>
<p>which agrees closely with the result from Habermann.</p>
<p>Another possible artifact is that we do not simulate an infinitely long
cylinder. This turns out to be a small effect. We use a cylinder with a
@@ -67,8 +83,8 @@
cylinder was twice as tall, and the results were essentially unchanged.</p>
<p>The errors in the computed velocity compared to the Faxen solution
are plotted in <a class="reference internal" href="#figure-2">Figure 2</a>. These were done with resolutions of
-8 × 16 × 8, 16 × 32 × 16, and 64 × 128 × 64,
-corresponding to grid sizes ([;h;]) of 0.25, 0.125, and 0.0625. Because
+8 × 16 × 8, 16 × 32 × 16, 32 × 64 × 32, and 64 × 128 × 64,
+corresponding to grid sizes ([;h;]) of 0.5, 0.25, 0.125, and 0.0625. Because
of the symmetries of the problem we only have to simulate a quarter
of the domain. As we increase the resolution (decrease [;h;]),
the error decreases. Since we are simulating a high viscosity sphere
@@ -88,7 +104,7 @@
<div align="center" class="figure">
<img alt="images/Sphere_Scaled_Error.png" src="images/Sphere_Scaled_Error.png" />
<p class="caption"><span class="target" id="figure-3">Figure 3</span>:
-As in figure [fig:Error-in-velocity], but with
+As in <cite>Figure 2</cite>, but with
the error scaled with [;h;]. So the higher resolution
errors are multiplied by 2, 4 and 8.</p>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -53,7 +53,9 @@
where
- [;f_H\\left(\\frac{r}{R}\\right)=-2.1050(r/R)+2.0865(r/R)^3-1.7068(r/R)^5+0.72603(r/R)^6.;]
+ [;f_H\\left(\\frac{r}{R}\\right) =
+ -2.1050(r/R) + 2.0865(r/R)^3
+ -1.7068(r/R)^5+0.72603(r/R)^6.;]
For our case with [;r=1;], [;R=4;], this gives a velocity of
@@ -67,8 +69,13 @@
where
-big equation
+ [;\\begin{eqnarray*}
+ f_f\\left(r/R\\right)=&-&2.10444(r/R)+2.08877
+ (r/R)^3-0.94813(r/R)^5 \\\\
+ &-&1.372(r/R)^6+3.87(r/R)^8-4.19(r/R)^{10}.
+ \\end{eqnarray*};]
+
For our case, this gives a speed of
[;u=1.12293603939\\cdot{10^{-3}},;]
@@ -82,8 +89,8 @@
The errors in the computed velocity compared to the Faxen solution
are plotted in `Figure 2`_. These were done with resolutions of
-8 |times| 16 |times| 8, 16 |times| 32 |times| 16, and 64 |times| 128 |times| 64,
-corresponding to grid sizes ([;h;]) of 0.25, 0.125, and 0.0625. Because
+8 |times| 16 |times| 8, 16 |times| 32 |times| 16, 32 |times| 64 |times| 32, and 64 |times| 128 |times| 64,
+corresponding to grid sizes ([;h;]) of 0.5, 0.25, 0.125, and 0.0625. Because
of the symmetries of the problem we only have to simulate a quarter
of the domain. As we increase the resolution (decrease [;h;]),
the error decreases. Since we are simulating a high viscosity sphere
@@ -110,7 +117,7 @@
:align: center
_`Figure 3`:
- As in figure [fig:Error-in-velocity], but with
+ As in `Figure 2`, but with
the error scaled with [;h;]. So the higher resolution
errors are multiplied by 2, 4 and 8.
Modified: doc/geodynamics.org/benchmarks/trunk/long/geomod2004.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/geomod2004.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/geomod2004.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Geomod 2004</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="geomod-2004">
-<h1 class="title">Geomod 2004</h1>
+<div class="document">
+
<p>Two benchmarks were created to validate numerical codes against analog
sandbox experiments [Buiter et al Numerical Sandbox]: one benchmark
simulates extension, and the other simulates shortening. A number of
@@ -19,8 +19,7 @@
standard against which to compare.</p>
<div class="section" id="extension">
<h1>Extension</h1>
-<p>This benchmark simulates a sandbox being extended as in Figure
-[fig:Extension-model-setup]. The right side and half of the bottom are
+<p>This benchmark simulates a sandbox being extended as in <a class="reference internal" href="#figure-1">Figure 1</a>. The right side and half of the bottom are
translated to the right. This creates a velocity discontinuity at the
center which is the initial seed for localization. Gale's implementation
of this benchmark is in <tt class="docutils literal"><span class="pre">input/benchmarks/extension.xml</span></tt>.</p>
@@ -28,27 +27,26 @@
included. Rather, the material is held fixed to the bottom boundary, and
the velocity discontinuity is smoothed over 0.2 cm. In addition, the
exact background viscosity is not prescribed by the benchmark. We have
-used 10<sup>12</sup> Pa-s, the same as used in the I2ELVIS calculations.
+used [;10^{12}Pa\cdot{s};], the same as used in the I2ELVIS calculations.
This value is somewhere in the middle of the range of values used in the
calculations for other codes.</p>
<!-- fig:Extension-model-setup -->
<div align="center" class="figure">
<img alt="images/Extension_setup.png" src="images/Extension_setup.png" style="width: 650px;" />
-<p class="caption">Extension model setup. Reproduced, with permission, from Buiter et al.
+<p class="caption"><span class="target" id="figure-1">Figure 1</span>: Extension model setup. Reproduced, with permission, from Buiter et al.
[Buiter et al Numerical Sandbox]</p>
</div>
-<p>A comparison against the other codes is in Figure
-[fig:Comparison-extension]. While it is difficult to perform exact
+<p>A comparison against the other codes is in <a class="reference internal" href="#figure-2">Figure 2</a>. While it is difficult to perform exact
comparisons, Gale produces similar fault patterns. It is interesting to
note that this qualitative comparison holds true even though the code is
-not exactly convergent. For example, Figure [fig:extension-convergence]
+not exactly convergent. For example, <a class="reference internal" href="#figure-3">Figure 3</a>
shows a run with varying resolution. Changing the resolution alters the
-details, but, after a certain minimum resolution, does not change the
+details, but after a certain minimum resolution, does not change the
character of the solution.</p>
<!-- fig:Comparison-extension -->
<div align="center" class="figure">
-<img alt="images/Extension_comparision.png" src="images/Extension_comparision.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the numerical extension models after 5 cm of
+<img alt="images/Extension_comparison.png" src="images/Extension_comparison.png" style="width: 600px;" />
+<p class="caption"><span class="target" id="figure-2">Figure 2</span>: Strain rate invariant for the numerical extension models after 5 cm of
extension. The resolutions of the various models are:
I2ELVIS: 400 × 75,
LAPEX-2D: 301 × 71,
@@ -56,21 +54,20 @@
SloMo: 401 × 71,
Sopale: 401 × 71,
Gale: 1024 × 128.
-Uper images reproduced, with permission, from Buiter et al.
+Upper images reproduced, with permission, from Buiter et al.
[Buiter et al Numerical Sandbox].</p>
</div>
<!-- fig:extension-convergence -->
<div align="center" class="figure">
<img alt="images/extension_sensitivity.png" src="images/extension_sensitivity.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the extension model after 5 cm of extension
+<p class="caption"><span class="target" id="figure-3">Figure 3</span>: Strain rate invariant for the extension model after 5 cm of extension
for four different resolutions: (a) 128 × 16, (b) 256 × 32,
(c) 512 × 64, and (d) 1024 × 128.</p>
</div>
</div>
<div class="section" id="shortening">
<h1>Shortening</h1>
-<p>This benchmark simulates a sandbox being shortened as in Figure
-[fig:Shortening-model-setup]. The right side is moved to the left,
+<p>This benchmark simulates a sandbox being shortened as in <a class="reference internal" href="#figure-4">Figure 4</a>. The right side is moved to the left,
creating a velocity discontinuity at the bottom right corner. Gale's
implementation of this benchmark is in <tt class="docutils literal"><span class="pre">input/benchmarks/shortening.xml</span></tt>.</p>
<p>Like most of the codes in the benchmark, we applied diffusion (diffusion
@@ -78,23 +75,23 @@
slope angles. This lies within the range used in calculations used by the
other codes (LAPEX-2D: 10<sup>-6</sup> m<sup>2</sup> s<sup>-1</sup>, Microfem: unspecified,
Sopale: 10<sup>-9</sup> m<sup>2</sup> s<sup>-1</sup>). Again, the exact background viscosity is
-not prescribed by the benchmark, so we have used 10<sup>12</sup> Pa-s.</p>
+not prescribed by the benchmark, so we have used [;10^{12}Pa\cdot{s};].</p>
<!-- fig:Shortening-model-setup -->
<div align="center" class="figure">
<img alt="images/Shortening_setup.png" src="images/Shortening_setup.png" style="width: 650px;" />
-<p class="caption">Shortening model setup. Reproduced, with permission, from Buiter et al.
+<p class="caption"><span class="target" id="figure-4">Figure 4</span>: Shortening model setup. Reproduced, with permission, from Buiter et al.
[Buiter et al Numerical Sandbox].</p>
</div>
<p>A comparison against the other codes' calculations at 14 cm of cumulative
-shortening is in Figure [fig:shortening-compare]. There is more variance
+shortening is in <a class="reference internal" href="#figure-5">Figure 5</a>. There is more variance
among the different codes, so it is difficult to tell whether Gale's
-behavior agrees with the other codes. Figure [fig:shortening-convergence]
+behavior agrees with the other codes. <a class="reference internal" href="#figure-6">Figure 6</a>
shows a run with a few different resolutions, and even there we see
marked differences in behavior as we increase resolution.</p>
<!-- fig:shortening-compare -->
<div align="center" class="figure">
<img alt="images/Shortening_comparison.png" src="images/Shortening_comparison.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the numerical shortening models after 14 cm
+<p class="caption"><span class="target" id="figure-5">Figure 5</span>: Strain rate invariant for the numerical shortening models after 14 cm
of shortening. The resolutions of the various models are:
I2ELVIS: 900 × 75,
LAPEX-2D: 351 × 71,
@@ -107,7 +104,7 @@
<!-- fig:shortening-convergence -->
<div align="center" class="figure">
<img alt="images/shortening_sensitivity.png" src="images/shortening_sensitivity.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the shortening model after 14 cm of
+<p class="caption"><span class="target" id="figure-6">Figure 6</span>: Strain rate invariant for the shortening model after 14 cm of
shortening for three different resolutions: (a) 128 × 32,
(b) 256 × 64, (c) 512 × 128.</p>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/long/geomod2004.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/geomod2004.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/geomod2004.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,3 @@
-
-===========
-Geomod 2004
-===========
-
Two benchmarks were created to validate numerical codes against analog
sandbox experiments [Buiter et al Numerical Sandbox]: one benchmark
simulates extension, and the other simulates shortening. A number of
@@ -13,8 +8,7 @@
Extension
=========
-This benchmark simulates a sandbox being extended as in Figure
-[fig:Extension-model-setup]. The right side and half of the bottom are
+This benchmark simulates a sandbox being extended as in `Figure 1`_. The right side and half of the bottom are
translated to the right. This creates a velocity discontinuity at the
center which is the initial seed for localization. Gale's implementation
of this benchmark is in ``input/benchmarks/extension.xml``.
@@ -23,7 +17,7 @@
included. Rather, the material is held fixed to the bottom boundary, and
the velocity discontinuity is smoothed over 0.2 cm. In addition, the
exact background viscosity is not prescribed by the benchmark. We have
-used 10\ :sup:`12` Pa-s, the same as used in the I2ELVIS calculations.
+used [;10^{12}Pa\\cdot{s};], the same as used in the I2ELVIS calculations.
This value is somewhere in the middle of the range of values used in the
calculations for other codes.
@@ -32,24 +26,23 @@
:align: center
:width: 650
- Extension model setup. Reproduced, with permission, from Buiter et al.
+ _`Figure 1`: Extension model setup. Reproduced, with permission, from Buiter et al.
[Buiter et al Numerical Sandbox]
-A comparison against the other codes is in Figure
-[fig:Comparison-extension]. While it is difficult to perform exact
+A comparison against the other codes is in `Figure 2`_. While it is difficult to perform exact
comparisons, Gale produces similar fault patterns. It is interesting to
note that this qualitative comparison holds true even though the code is
-not exactly convergent. For example, Figure [fig:extension-convergence]
+not exactly convergent. For example, `Figure 3`_
shows a run with varying resolution. Changing the resolution alters the
-details, but, after a certain minimum resolution, does not change the
+details, but after a certain minimum resolution, does not change the
character of the solution.
.. fig:Comparison-extension
-.. figure:: images/Extension_comparision.png
+.. figure:: images/Extension_comparison.png
:align: center
:width: 600
- Strain rate invariant for the numerical extension models after 5 cm of
+ _`Figure 2`: Strain rate invariant for the numerical extension models after 5 cm of
extension. The resolutions of the various models are:
I2ELVIS: 400 |times| 75,
LAPEX-2D: 301 |times| 71,
@@ -57,7 +50,7 @@
SloMo: 401 |times| 71,
Sopale: 401 |times| 71,
Gale: 1024 |times| 128.
- Uper images reproduced, with permission, from Buiter et al.
+ Upper images reproduced, with permission, from Buiter et al.
[Buiter et al Numerical Sandbox].
.. fig:extension-convergence
@@ -65,7 +58,7 @@
:align: center
:width: 600
- Strain rate invariant for the extension model after 5 cm of extension
+ _`Figure 3`: Strain rate invariant for the extension model after 5 cm of extension
for four different resolutions: (a) 128 |times| 16, (b) 256 |times| 32,
(c) 512 |times| 64, and (d) 1024 |times| 128.
@@ -73,8 +66,7 @@
Shortening
==========
-This benchmark simulates a sandbox being shortened as in Figure
-[fig:Shortening-model-setup]. The right side is moved to the left,
+This benchmark simulates a sandbox being shortened as in `Figure 4`_. The right side is moved to the left,
creating a velocity discontinuity at the bottom right corner. Gale's
implementation of this benchmark is in ``input/benchmarks/shortening.xml``.
@@ -83,20 +75,20 @@
slope angles. This lies within the range used in calculations used by the
other codes (LAPEX-2D: 10\ :sup:`-6` |diffusion-units|, Microfem: unspecified,
Sopale: 10\ :sup:`-9` |diffusion-units|). Again, the exact background viscosity is
-not prescribed by the benchmark, so we have used 10\ :sup:`12` Pa-s.
+not prescribed by the benchmark, so we have used [;10^{12}Pa\\cdot{s};].
.. fig:Shortening-model-setup
.. figure:: images/Shortening_setup.png
:align: center
:width: 650
- Shortening model setup. Reproduced, with permission, from Buiter et al.
+ _`Figure 4`: Shortening model setup. Reproduced, with permission, from Buiter et al.
[Buiter et al Numerical Sandbox].
A comparison against the other codes' calculations at 14 cm of cumulative
-shortening is in Figure [fig:shortening-compare]. There is more variance
+shortening is in `Figure 5`_. There is more variance
among the different codes, so it is difficult to tell whether Gale's
-behavior agrees with the other codes. Figure [fig:shortening-convergence]
+behavior agrees with the other codes. `Figure 6`_
shows a run with a few different resolutions, and even there we see
marked differences in behavior as we increase resolution.
@@ -105,7 +97,7 @@
:align: center
:width: 600
- Strain rate invariant for the numerical shortening models after 14 cm
+ _`Figure 5`: Strain rate invariant for the numerical shortening models after 14 cm
of shortening. The resolutions of the various models are:
I2ELVIS: 900 |times| 75,
LAPEX-2D: 351 |times| 71,
@@ -120,7 +112,7 @@
:align: center
:width: 600
- Strain rate invariant for the shortening model after 14 cm of
+ _`Figure 6`: Strain rate invariant for the shortening model after 14 cm of
shortening for three different resolutions: (a) 128 |times| 32,
(b) 256 |times| 64, (c) 512 |times| 128.
Modified: doc/geodynamics.org/benchmarks/trunk/long/geomod2008.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/geomod2008.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/geomod2008.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,21 +4,20 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Geomod 2008</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="geomod-2008">
-<h1 class="title">Geomod 2008</h1>
+<div class="document">
+
<p>Using the lessons learned from the Geomod 2004 benchmarks, new
benchmarks were created that would make it easier to compare numerical
experiments with each other and with analog experiments [Geomod 2008].</p>
<div class="section" id="stable-wedge">
<h1>Stable Wedge</h1>
-<p>This benchmark simulates a wall pushing a wedge as in Figure
-[fig:Wedge_setup]. There is an analytic solution [Dahlen Wedge] which
+<p>This benchmark simulates a wall pushing a wedge as in <a class="reference internal" href="#figure-1">Figure 1</a>. There is an analytic solution [Dahlen Wedge] which
details what the friction on the bottom and sides should be to provide
enough resistance so that the wedge does not collapse under its own
weight, but not so much as to cause any internal deformation as it
@@ -36,26 +35,26 @@
internal angle of friction is 36° weakening to 31°, while
in the element at the boundary the internal angle of friction is
16° weakening to 14°. Similarly, in the bulk, the
-cohesion is 10 Pa, while at the boundary the cohesion is 10 Pa
-weakening to 0.01 Pa. If we do not weaken the cohesion, when we try to
+cohesion is 10 [;Pa;], while at the boundary the cohesion is 10 [;Pa;]
+weakening to 0.01 [;Pa;]. If we do not weaken the cohesion, when we try to
model an unstable wedge by reducing the internal angle of friction, the
wedge never collapses on itself.</p>
-<p>Figure [fig:Stable_sri] shows the strain rate invariant after the wall
-has moved 4 cm, and Figure [fig:Stable_particles] shows the particles.
+<p><a class="reference internal" href="#figure-2">Figure 2</a> shows the strain rate invariant after the wall
+has moved 4 cm, and <a class="reference internal" href="#figure-3">Figure 3</a> shows the particles.
The bulk translates with almost no deformation, although, as expected,
the tip deforms. The odd structures at the tip are below the grid
-resolution. Figure [fig:Stable_unstable] shows a simulation when we
+resolution. <a class="reference internal" href="#figure-4">Figure 4</a> shows a simulation when we
reduce the boundary friction to 1°. The wedge quickly becomes
unstable and collapses.</p>
<!-- fig:Wedge_setup -->
<div align="center" class="figure">
<img alt="images/Geomod2008_wedge_setup.png" src="images/Geomod2008_wedge_setup.png" />
-<p class="caption">Setup for the stable wedge benchmark. Image courtesy of Susanne Buiter.</p>
+<p class="caption"><span class="target" id="figure-1">Figure 1</span>: Setup for the stable wedge benchmark. Image courtesy of Susanne Buiter.</p>
</div>
<!-- fig:Stable_sri -->
<div align="center" class="figure">
<img alt="images/Stable_wedge_sri.png" src="images/Stable_wedge_sri.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the stable wedge benchmark within the wedge.
+<p class="caption"><span class="target" id="figure-2">Figure 2</span>: Strain rate invariant for the stable wedge benchmark within the wedge.
Outside the wedge, the strain rates are large because of the air's low
viscosity. The resolution is 512 × 128, and the wedge has translated
4 cm.</p>
@@ -63,7 +62,7 @@
<!-- fig:Stable_particles -->
<div align="center" class="figure">
<img alt="images/Stable_wedge_particles.png" src="images/Stable_wedge_particles.png" style="width: 600px;" />
-<p class="caption">Material particles for the stable wedge benchmark. The deformation at
+<p class="caption"><span class="target" id="figure-3">Figure 3</span>: Material particles for the stable wedge benchmark. The deformation at
the tip is caused by a finite boundary cohesion, although the actual
structure is not resolved. The resolution is 512 × 128, and the
wedge has translated 4 cm.</p>
@@ -71,9 +70,9 @@
<!-- fig:Stable_unstable -->
<div align="center" class="figure">
<img alt="images/Stable_wedge_unstable.png" src="images/Stable_wedge_unstable.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant and velocity arrows for the stable wedge
-benchmark, but with the friction angle reduced to 1°. Note that
-the strain rates are much higher than in Figure [fig:Stable_sri]. The
+<p class="caption"><span class="target" id="figure-4">Figure 4</span>: Strain rate invariant and velocity arrows for the stable wedge
+benchmark, but with the boundary friction angle reduced to 1°. Note that
+the strain rates are much higher than in Figure 2. The
wedge collapses almost immediately. The resolution is 512 × 128,
and the wedge has translated 0.17 cm.</p>
</div>
@@ -81,61 +80,61 @@
<div class="section" id="unstable-shortening">
<h1>Unstable Shortening</h1>
<p>This benchmark simulates a wall pushing against a wall of sand as in
-Figure [fig:Unstable-setup]. There are three layers of sand, with the
+<a class="reference internal" href="#figure-5">Figure 5</a>. There are three layers of sand, with the
middle layer being a little heavier and sticking a little more to the
-boundary. Otherwise it is identical. Figures
-[fig:unstable_sri_128],
-[fig:unstable_sri_256],
-[fig:unstable_sri_512],
-[fig:unstable_particles_128],
-[fig:unstable_particles_256], and
-[fig:unstable_particles_512] show results at different times and
+boundary. Otherwise it is identical.
+<a class="reference internal" href="#figure-6">Figure 6</a>,
+<a class="reference internal" href="#figure-7">Figure 7</a>,
+<a class="reference internal" href="#figure-8">Figure 8</a>,
+<a class="reference internal" href="#figure-9">Figure 9</a>,
+<a class="reference internal" href="#figure-10">Figure 10</a>, and
+<a class="reference internal" href="#figure-11">Figure 11</a> show results at different times and
different resolutions.</p>
<!-- fig:Unstable-setup -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_setup.png" src="images/Geomod2008_unstable_setup.png" />
-<p class="caption">Setup for the unstable shortening benchmark.
+<p class="caption"><span class="target" id="figure-5">Figure 5</span>: Setup for the unstable shortening benchmark.
Image courtesy of Susanne Buiter.</p>
</div>
<!-- fig:unstable_sri_128 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_sri128x32.png" src="images/Geomod2008_unstable_sri128x32.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the unstable shortening benchmark with a
+<p class="caption"><span class="target" id="figure-6">Figure 6</span>: Strain rate invariant for the unstable shortening benchmark with a
resolution of 128 × 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:unstable_sri_256 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_sri256x64.png" src="images/Geomod2008_unstable_sri256x64.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the unstable shortening benchmark with a
+<p class="caption"><span class="target" id="figure-7">Figure 7</span>: Strain rate invariant for the unstable shortening benchmark with a
resolution of 256 × 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:unstable_sri_512 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_sri512x128.png" src="images/Geomod2008_unstable_sri512x128.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the unstable shortening benchmark with a
+<p class="caption"><span class="target" id="figure-8">Figure 8</span>: Strain rate invariant for the unstable shortening benchmark with a
resolution of 512 × 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:unstable_particles_128 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_particles128x32.png" src="images/Geomod2008_unstable_particles128x32.png" style="width: 600px;" />
-<p class="caption">Material particles for the unstable shortening benchmark with a
+<p class="caption"><span class="target" id="figure-9">Figure 9</span>: Material particles for the unstable shortening benchmark with a
resolution of 128 × 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:unstable_particles_256 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_particles256x64.png" src="images/Geomod2008_unstable_particles256x64.png" style="width: 600px;" />
-<p class="caption">Material particles for the unstable shortening benchmark with a
+<p class="caption"><span class="target" id="figure-10">Figure 10</span>: Material particles for the unstable shortening benchmark with a
resolution of 256 × 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:unstable_particles_512 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_unstable_particles512x128.png" src="images/Geomod2008_unstable_particles512x128.png" style="width: 600px;" />
-<p class="caption">Material particles for the unstable shortening benchmark with a
+<p class="caption"><span class="target" id="figure-11">Figure 11</span>: Material particles for the unstable shortening benchmark with a
resolution of 512 × 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
@@ -144,61 +143,60 @@
<h1>Brittle Shortening</h1>
<p>This benchmark is very similar to unstable shortening. The only
difference is that part of the bottom is also moving along as shown in
-Figure [fig:Brittle_setup]. This causes the deformation to start from
+Figure <a class="reference internal" href="#figure-12">Figure 12</a>. This causes the deformation to start from
inside the sand box, rather than along the walls.
-Figures
-[fig:brittle_sri_128],
-[fig:brittle_sri_256],
-[fig:brittle_sri_512],
-[fig:brittle_particles_128],
-[fig:brittle_particles_256], and
-[fig:brittle_particles_512] show results at different times and
+<a class="reference internal" href="#figure-13">Figure 13</a>,
+<a class="reference internal" href="#figure-14">Figure 14</a>,
+<a class="reference internal" href="#figure-15">Figure 15</a>,
+<a class="reference internal" href="#figure-16">Figure 16</a>,
+<a class="reference internal" href="#figure-17">Figure 17</a>, and
+<a class="reference internal" href="#figure-18">Figure 18</a> show results at different times and
different resolutions.</p>
<!-- fig:Brittle_setup -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_setup.png" src="images/Geomod2008_brittle_setup.png" />
-<p class="caption">Setup for the brittle shortening benchmark.
+<p class="caption"><span class="target" id="figure-12">Figure 12</span>: Setup for the brittle shortening benchmark.
Image courtesy of Susanne Buiter.</p>
</div>
<!-- fig:brittle_sri_128 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_sri128x32.png" src="images/Geomod2008_brittle_sri128x32.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the brittle shortening benchmark with a
+<p class="caption"><span class="target" id="figure-13">Figure 13</span>: Strain rate invariant for the brittle shortening benchmark with a
resolution of 128 × 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:brittle_sri_256 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_sri256x64.png" src="images/Geomod2008_brittle_sri256x64.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the brittle shortening benchmark with a
+<p class="caption"><span class="target" id="figure-14">Figure 14</span>: Strain rate invariant for the brittle shortening benchmark with a
resolution of 256 × 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:brittle_sri_512 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_sri512x128.png" src="images/Geomod2008_brittle_sri512x128.png" style="width: 600px;" />
-<p class="caption">Strain rate invariant for the brittle shortening benchmark with a
+<p class="caption"><span class="target" id="figure-15">Figure 15</span>: Strain rate invariant for the brittle shortening benchmark with a
resolution of 512 × 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:brittle_particles_128 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_particles128x32.png" src="images/Geomod2008_brittle_particles128x32.png" style="width: 600px;" />
-<p class="caption">Material particles for the brittle shortening benchmark with a
+<p class="caption"><span class="target" id="figure-16">Figure 16</span>: Material particles for the brittle shortening benchmark with a
resolution of 128 × 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:brittle_particles_256 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_particles256x64.png" src="images/Geomod2008_brittle_particles256x64.png" style="width: 600px;" />
-<p class="caption">Material particles for the brittle shortening benchmark with a
+<p class="caption"><span class="target" id="figure-17">Figure 17</span>: Material particles for the brittle shortening benchmark with a
resolution of 256 × 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
<!-- fig:brittle_particles_512 -->
<div align="center" class="figure">
<img alt="images/Geomod2008_brittle_particles512x128.png" src="images/Geomod2008_brittle_particles512x128.png" style="width: 600px;" />
-<p class="caption">Material particles for the brittle shortening benchmark with a
+<p class="caption"><span class="target" id="figure-18">Figure 18</span>: Material particles for the brittle shortening benchmark with a
resolution of 512 × 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.</p>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/long/geomod2008.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/geomod2008.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/geomod2008.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,3 @@
-
-===========
-Geomod 2008
-===========
-
Using the lessons learned from the Geomod 2004 benchmarks, new
benchmarks were created that would make it easier to compare numerical
experiments with each other and with analog experiments [Geomod 2008].
@@ -11,8 +6,7 @@
Stable Wedge
============
-This benchmark simulates a wall pushing a wedge as in Figure
-[fig:Wedge_setup]. There is an analytic solution [Dahlen Wedge] which
+This benchmark simulates a wall pushing a wedge as in `Figure 1`_. There is an analytic solution [Dahlen Wedge] which
details what the friction on the bottom and sides should be to provide
enough resistance so that the wedge does not collapse under its own
weight, but not so much as to cause any internal deformation as it
@@ -32,16 +26,16 @@
internal angle of friction is 36\ |deg| weakening to 31\ |deg|, while
in the element at the boundary the internal angle of friction is
16\ |deg| weakening to 14\ |deg|. Similarly, in the bulk, the
-cohesion is 10 Pa, while at the boundary the cohesion is 10 Pa
-weakening to 0.01 Pa. If we do not weaken the cohesion, when we try to
+cohesion is 10 [;Pa;], while at the boundary the cohesion is 10 [;Pa;]
+weakening to 0.01 [;Pa;]. If we do not weaken the cohesion, when we try to
model an unstable wedge by reducing the internal angle of friction, the
wedge never collapses on itself.
-Figure [fig:Stable_sri] shows the strain rate invariant after the wall
-has moved 4 cm, and Figure [fig:Stable_particles] shows the particles.
+`Figure 2`_ shows the strain rate invariant after the wall
+has moved 4 cm, and `Figure 3`_ shows the particles.
The bulk translates with almost no deformation, although, as expected,
the tip deforms. The odd structures at the tip are below the grid
-resolution. Figure [fig:Stable_unstable] shows a simulation when we
+resolution. `Figure 4`_ shows a simulation when we
reduce the boundary friction to 1\ |deg|. The wedge quickly becomes
unstable and collapses.
@@ -50,14 +44,14 @@
.. figure:: images/Geomod2008_wedge_setup.png
:align: center
- Setup for the stable wedge benchmark. Image courtesy of Susanne Buiter.
+ _`Figure 1`: Setup for the stable wedge benchmark. Image courtesy of Susanne Buiter.
.. fig:Stable_sri
.. figure:: images/Stable_wedge_sri.png
:align: center
:width: 600
- Strain rate invariant for the stable wedge benchmark within the wedge.
+ _`Figure 2`: Strain rate invariant for the stable wedge benchmark within the wedge.
Outside the wedge, the strain rates are large because of the air's low
viscosity. The resolution is 512 |times| 128, and the wedge has translated
4 cm.
@@ -68,7 +62,7 @@
:align: center
:width: 600
- Material particles for the stable wedge benchmark. The deformation at
+ _`Figure 3`: Material particles for the stable wedge benchmark. The deformation at
the tip is caused by a finite boundary cohesion, although the actual
structure is not resolved. The resolution is 512 |times| 128, and the
wedge has translated 4 cm.
@@ -78,9 +72,9 @@
:align: center
:width: 600
- Strain rate invariant and velocity arrows for the stable wedge
- benchmark, but with the friction angle reduced to 1\ |deg|. Note that
- the strain rates are much higher than in Figure [fig:Stable_sri]. The
+ _`Figure 4`: Strain rate invariant and velocity arrows for the stable wedge
+ benchmark, but with the boundary friction angle reduced to 1\ |deg|. Note that
+ the strain rates are much higher than in Figure 2. The
wedge collapses almost immediately. The resolution is 512 |times| 128,
and the wedge has translated 0.17 cm.
@@ -89,15 +83,15 @@
===================
This benchmark simulates a wall pushing against a wall of sand as in
-Figure [fig:Unstable-setup]. There are three layers of sand, with the
+`Figure 5`_. There are three layers of sand, with the
middle layer being a little heavier and sticking a little more to the
-boundary. Otherwise it is identical. Figures
-[fig:unstable_sri_128],
-[fig:unstable_sri_256],
-[fig:unstable_sri_512],
-[fig:unstable_particles_128],
-[fig:unstable_particles_256], and
-[fig:unstable_particles_512] show results at different times and
+boundary. Otherwise it is identical.
+`Figure 6`_,
+`Figure 7`_,
+`Figure 8`_,
+`Figure 9`_,
+`Figure 10`_, and
+`Figure 11`_ show results at different times and
different resolutions.
@@ -105,7 +99,7 @@
.. figure:: images/Geomod2008_unstable_setup.png
:align: center
- Setup for the unstable shortening benchmark.
+ _`Figure 5`: Setup for the unstable shortening benchmark.
Image courtesy of Susanne Buiter.
.. fig:unstable_sri_128
@@ -113,7 +107,7 @@
:align: center
:width: 600
- Strain rate invariant for the unstable shortening benchmark with a
+ _`Figure 6`: Strain rate invariant for the unstable shortening benchmark with a
resolution of 128 |times| 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -122,7 +116,7 @@
:align: center
:width: 600
- Strain rate invariant for the unstable shortening benchmark with a
+ _`Figure 7`: Strain rate invariant for the unstable shortening benchmark with a
resolution of 256 |times| 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -131,7 +125,7 @@
:align: center
:width: 600
- Strain rate invariant for the unstable shortening benchmark with a
+ _`Figure 8`: Strain rate invariant for the unstable shortening benchmark with a
resolution of 512 |times| 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -140,7 +134,7 @@
:align: center
:width: 600
- Material particles for the unstable shortening benchmark with a
+ _`Figure 9`: Material particles for the unstable shortening benchmark with a
resolution of 128 |times| 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -149,7 +143,7 @@
:align: center
:width: 600
- Material particles for the unstable shortening benchmark with a
+ _`Figure 10`: Material particles for the unstable shortening benchmark with a
resolution of 256 |times| 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -158,7 +152,7 @@
:align: center
:width: 600
- Material particles for the unstable shortening benchmark with a
+ _`Figure 11`: Material particles for the unstable shortening benchmark with a
resolution of 512 |times| 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -168,22 +162,21 @@
This benchmark is very similar to unstable shortening. The only
difference is that part of the bottom is also moving along as shown in
-Figure [fig:Brittle_setup]. This causes the deformation to start from
+Figure `Figure 12`_. This causes the deformation to start from
inside the sand box, rather than along the walls.
-Figures
-[fig:brittle_sri_128],
-[fig:brittle_sri_256],
-[fig:brittle_sri_512],
-[fig:brittle_particles_128],
-[fig:brittle_particles_256], and
-[fig:brittle_particles_512] show results at different times and
+`Figure 13`_,
+`Figure 14`_,
+`Figure 15`_,
+`Figure 16`_,
+`Figure 17`_, and
+`Figure 18`_ show results at different times and
different resolutions.
.. fig:Brittle_setup
.. figure:: images/Geomod2008_brittle_setup.png
:align: center
- Setup for the brittle shortening benchmark.
+ _`Figure 12`: Setup for the brittle shortening benchmark.
Image courtesy of Susanne Buiter.
.. fig:brittle_sri_128
@@ -191,7 +184,7 @@
:align: center
:width: 600
- Strain rate invariant for the brittle shortening benchmark with a
+ _`Figure 13`: Strain rate invariant for the brittle shortening benchmark with a
resolution of 128 |times| 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -200,7 +193,7 @@
:align: center
:width: 600
- Strain rate invariant for the brittle shortening benchmark with a
+ _`Figure 14`: Strain rate invariant for the brittle shortening benchmark with a
resolution of 256 |times| 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -209,7 +202,7 @@
:align: center
:width: 600
- Strain rate invariant for the brittle shortening benchmark with a
+ _`Figure 15`: Strain rate invariant for the brittle shortening benchmark with a
resolution of 512 |times| 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -218,7 +211,7 @@
:align: center
:width: 600
- Material particles for the brittle shortening benchmark with a
+ _`Figure 16`: Material particles for the brittle shortening benchmark with a
resolution of 128 |times| 32. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -227,7 +220,7 @@
:align: center
:width: 600
- Material particles for the brittle shortening benchmark with a
+ _`Figure 17`: Material particles for the brittle shortening benchmark with a
resolution of 256 |times| 64. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
@@ -236,7 +229,7 @@
:align: center
:width: 600
- Material particles for the brittle shortening benchmark with a
+ _`Figure 18`: Material particles for the brittle shortening benchmark with a
resolution of 512 |times| 128. The snapshots are taken
at 0, 2.5, 5, 7.5, and 10 cm of shortening.
Modified: doc/geodynamics.org/benchmarks/trunk/long/index.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/index.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/index.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Benchmarks</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="benchmarks">
-<h1 class="title">Benchmarks</h1>
+<div class="document">
+
<ul class="simple">
<li><a class="reference external" href="falling-sphere">Falling Sphere</a></li>
<li><a class="reference external" href="circular-inclusion">Circular Inclusion</a></li>
Modified: doc/geodynamics.org/benchmarks/trunk/long/index.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/index.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/index.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,7 +1,4 @@
-Benchmarks
-==========
-
* `Falling Sphere <falling-sphere>`_
* `Circular Inclusion <circular-inclusion>`_
Modified: doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,15 +4,15 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Relaxation of Topography</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="relaxation-of-topography">
-<h1 class="title">Relaxation of Topography</h1>
+<div class="document">
-<p>Given an infinitely deep purely viscous medium with an infinitesimal
+
+<p>Given an infinitely deep purely viscous medium with an infinitesimal initial
sinusoidal height profile, the topography will decay exponentially
with the timescale [Folds]</p>
<blockquote>
@@ -25,7 +25,7 @@
order [;(2\pi{A}/L)^2;], where [;A;] is the amplitude of the sinusoid.
We use [;L=1;] and [;A=0.01;], giving errors of order 0.02% and 0.4%.</p>
<p>The file <tt class="docutils literal"><span class="pre">input/benchmarks/sinusoid/README</span></tt> explains how to run this
-benchmark. Figure [fig:Strain-topo] shows the results of a low-resolution
+benchmark. <a class="reference internal" href="#figure-1">Figure 1</a> shows the results of a low-resolution
run. Even this run is not particularly small (128 × 256),
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
@@ -33,23 +33,23 @@
<!-- fig:Strain-topo -->
<div align="center" class="figure">
<img alt="images/Paraview_topography.png" src="images/Paraview_topography.png" style="width: 350px;" />
-<p class="caption">Strain rate and velocities for a sinusoidal topography relaxing
+<p class="caption"><span class="target" id="figure-1">Figure 1</span>. Strain rate and velocities for a sinusoidal topography relaxing
under gravity.</p>
</div>
<p>Running the code with multiple resolutions and measuring the error in the
-height in the trough gives Figure [fig:topo-error]. Scaling the error
-with resolution gives Figure [fig:scaled-topo-error]. The error decreases
+height in the trough gives <a class="reference internal" href="#figure-2">Figure 2</a>. Scaling the error
+with resolution gives <a class="reference internal" href="#figure-3">Figure 3</a>. The error decreases
linearly with increasing resolution, giving us confidence in our ability
to accurately track topography.</p>
<!-- fig:topo-error -->
<div align="center" class="figure">
<img alt="images/topo_error.png" src="images/topo_error.png" />
-<p class="caption">Error in the height at the trough</p>
+<p class="caption"><span class="target" id="figure-2">Figure 2</span>. Error in the height at the trough</p>
</div>
<!-- fig:scaled-topo-error -->
<div align="center" class="figure">
<img alt="images/topo_scaled_error.png" src="images/topo_scaled_error.png" />
-<p class="caption">As in Figure [fig:topo-error], but with the error scaled with [;h;].
+<p class="caption"><span class="target" id="figure-3">Figure 3</span>. As in <a class="reference internal" href="#figure-2">Figure 2</a>, but with the error scaled with [;h;].
So the medium-resolution error is multiplied by 2 and the
high-resolution error is multiplied by 4.</p>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,4 @@
-
-Relaxation of Topography
-========================
-
-Given an infinitely deep purely viscous medium with an infinitesimal
+Given an infinitely deep purely viscous medium with an infinitesimal initial
sinusoidal height profile, the topography will decay exponentially
with the timescale [Folds]
@@ -18,7 +14,7 @@
We use [;L=1;] and [;A=0.01;], giving errors of order 0.02% and 0.4%.
The file ``input/benchmarks/sinusoid/README`` explains how to run this
-benchmark. Figure [fig:Strain-topo] shows the results of a low-resolution
+benchmark. `Figure 1`_ shows the results of a low-resolution
run. Even this run is not particularly small (128 |times| 256),
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
@@ -29,12 +25,12 @@
:align: center
:width: 350
- Strain rate and velocities for a sinusoidal topography relaxing
+ _`Figure 1`. Strain rate and velocities for a sinusoidal topography relaxing
under gravity.
Running the code with multiple resolutions and measuring the error in the
-height in the trough gives Figure [fig:topo-error]. Scaling the error
-with resolution gives Figure [fig:scaled-topo-error]. The error decreases
+height in the trough gives `Figure 2`_. Scaling the error
+with resolution gives `Figure 3`_. The error decreases
linearly with increasing resolution, giving us confidence in our ability
to accurately track topography.
@@ -42,13 +38,13 @@
.. figure:: images/topo_error.png
:align: center
- Error in the height at the trough
+ _`Figure 2`. Error in the height at the trough
.. fig:scaled-topo-error
.. figure:: images/topo_scaled_error.png
:align: center
- As in Figure [fig:topo-error], but with the error scaled with [;h;].
+ _`Figure 3`. As in `Figure 2`_, but with the error scaled with [;h;].
So the medium-resolution error is multiplied by 2 and the
high-resolution error is multiplied by 4.
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/index.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/index.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/index.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,4 +1,3 @@
-
General Description of the Benchmark Problem
============================================
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Suite 1</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="suite-1">
-<h1 class="title">Suite 1</h1>
+<div class="document">
+
<p>Testing the implementation of driving forces, isoviscous, comparing with
analytical solutions.</p>
<p>The non-dimensional numbers are moderately low in this case (Ra=10^5,
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite1.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,7 +1,3 @@
-
-Suite 1
-=======
-
Testing the implementation of driving forces, isoviscous, comparing with
analytical solutions.
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,13 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Suite 2</title>
+<title>Steady state, basal heated</title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="suite-2">
-<h1 class="title">Suite 2</h1>
-<h2 class="subtitle" id="steady-state-basal-heated">Steady state, basal heated</h2>
+<div class="document" id="steady-state-basal-heated">
+<h1 class="title">Steady state, basal heated</h1>
<p>Gamma = 1.1 in this suite.</p>
<p>Temperature dependent viscosity: eta = exp(-5 * T)</p>
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite2.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,9 +1,3 @@
-
-=======
-Suite 2
-=======
-
-
Steady state, basal heated
==========================
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,13 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Suite 3</title>
+<title>Steady state, internal heated</title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="suite-3">
-<h1 class="title">Suite 3</h1>
-<h2 class="subtitle" id="steady-state-internal-heated">Steady state, internal heated</h2>
+<div class="document" id="steady-state-internal-heated">
+<h1 class="title">Steady state, internal heated</h1>
<p>This suite will have several cases taken from Jarvis and McKenzie (1980)</p>
<p>H = 1, no-heatflux for the bottom boundary.</p>
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite3.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,3 @@
-
-=======
-Suite 3
-=======
-
Steady state, internal heated
=============================
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,13 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>Suite 4</title>
+<title>Time-dependent, unstead convection</title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="suite-4">
-<h1 class="title">Suite 4</h1>
-<h2 class="subtitle" id="time-dependent-unstead-convection">Time-dependent, unstead convection</h2>
+<div class="document" id="time-dependent-unstead-convection">
+<h1 class="title">Time-dependent, unstead convection</h1>
<p>Parameters to be determined ...</p>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/2d-cartesian/suite4.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,3 @@
-
-=======
-Suite 4
-=======
-
Time-dependent, unstead convection
==================================
Modified: doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -4,14 +4,14 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
-<title>3D Spherical Mantle Convection Benchmarks</title>
+<title></title>
<script type="text/javascript" src="http://geodynamics.org/cig/portal_javascripts/Plone%20Default/textheworld6.user.js"></script>
<link rel="stylesheet" href="../../css/voidspace.css" type="text/css" />
</head>
<body>
-<div class="document" id="d-spherical-mantle-convection-benchmarks">
-<h1 class="title">3D Spherical Mantle Convection Benchmarks</h1>
+<div class="document">
+
<p>Presents initial benchmark results for CitcomS and comparisons with Stemmer et
al {2006} and Ratcliff et al {1996} and Yoshida and Kageyama {2004} when the
solutions are available from these codes. The community's comments and
Modified: doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/3d-spherical/index.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,8 +1,3 @@
-
-=========================================
-3D Spherical Mantle Convection Benchmarks
-=========================================
-
Presents initial benchmark results for CitcomS and comparisons with Stemmer et
al {2006} and Ratcliff et al {1996} and Yoshida and Kageyama {2004} when the
solutions are available from these codes. The community's comments and
Modified: doc/geodynamics.org/benchmarks/trunk/mc/index.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/index.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/index.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -35,9 +35,9 @@
<div class="section" id="other-links">
<h1>Other Links</h1>
<ul class="simple">
-<li><a class="reference external" href="http://geodynamics.org/cig/workinggroups/mc/workarea/benchmark/">Mantle Convection Benchmarks</a></li>
-<li><a class="reference external" href="http://geodynamics.org/cig/Members/tan2/benchmarks/">Benchmarks for 2D Cartesian Compressible Convection</a></li>
-<li><a class="reference external" href="http://geodynamics.org/cig/workinggroups/mc/workarea/benchmark/3dconvention/">3D Spherical Mantle Convection Benchmarks</a></li>
+<li><a class="reference external" href="/cig/workinggroups/mc/workarea/benchmark/">Mantle Convection Benchmarks</a></li>
+<li><a class="reference external" href="/cig/Members/tan2/benchmarks/">Benchmarks for 2D Cartesian Compressible Convection</a></li>
+<li><a class="reference external" href="/cig/workinggroups/mc/workarea/benchmark/3dconvention/">3D Spherical Mantle Convection Benchmarks</a></li>
</ul>
</div>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/mc/index.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/mc/index.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/mc/index.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,4 +1,3 @@
-
============================
Mantle Convection Benchmarks
============================
@@ -35,7 +34,7 @@
* `Benchmarks for 2D Cartesian Compressible Convection`__
* `3D Spherical Mantle Convection Benchmarks`__
-__ http://geodynamics.org/cig/workinggroups/mc/workarea/benchmark/
-__ http://geodynamics.org/cig/Members/tan2/benchmarks/
-__ http://geodynamics.org/cig/workinggroups/mc/workarea/benchmark/3dconvention/
+__ /cig/workinggroups/mc/workarea/benchmark/
+__ /cig/Members/tan2/benchmarks/
+__ /cig/workinggroups/mc/workarea/benchmark/3dconvention/
Modified: doc/geodynamics.org/benchmarks/trunk/short/index.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/short/index.html 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/short/index.html 2009-10-21 22:34:13 UTC (rev 15862)
@@ -12,7 +12,6 @@
<div class="document">
-<p>Short-Term Tectonics Benchmarks</p>
<p>"Overview":overview</p>
<p>Benchmarks</p>
<blockquote>
Modified: doc/geodynamics.org/benchmarks/trunk/short/index.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/short/index.rst 2009-10-21 20:06:05 UTC (rev 15861)
+++ doc/geodynamics.org/benchmarks/trunk/short/index.rst 2009-10-21 22:34:13 UTC (rev 15862)
@@ -1,6 +1,3 @@
-
-Short-Term Tectonics Benchmarks
-
"Overview":overview
Benchmarks
More information about the CIG-COMMITS
mailing list