[cig-commits] r15831 - doc/geodynamics.org/benchmarks/trunk/long

[luis at geodynamics.org]

Author: luis
Date: 2009-10-18 00:18:54 -0700 (Sun, 18 Oct 2009)
New Revision: 15831

Modified:
   doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html
   doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst
Log:
Updated long/falling-sphere.rst

Modified: doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html	2009-10-18 07:18:47 UTC (rev 15830)
+++ doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.html	2009-10-18 07:18:54 UTC (rev 15831)
@@ -65,16 +65,16 @@
 cylinder. This turns out to be a small effect. We use a cylinder with a
 height of 8, and place the sphere halfway down. We did runs where the
 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 \times 16 \times 8;], [;16 \times 32 \times 16;],
-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 rather than a
-completely rigid sphere, the velocity inside the sphere is not uniform.
-The error bars indicate the variation in velocity across the sphere.</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
+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
+rather than a completely rigid sphere, the velocity inside the sphere
+is not uniform. The error bars indicate the variation in velocity
+across the sphere.</p>
 <!-- fig:Error-in-velocity -->
 <div align="center" class="figure">
 <img alt="images/Sphere_Error.png" src="images/Sphere_Error.png" />

Modified: doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst	2009-10-18 07:18:47 UTC (rev 15830)
+++ doc/geodynamics.org/benchmarks/trunk/long/falling-sphere.rst	2009-10-18 07:18:54 UTC (rev 15831)
@@ -70,16 +70,16 @@
 height of 8, and place the sphere halfway down. We did runs where the
 cylinder was twice as tall, and the results were essentially unchanged.
 
-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 [;0.5;], [;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 rather than a
-completely rigid sphere, the velocity inside the sphere is not uniform.
-The error bars indicate the variation in velocity across the sphere.
+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
+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
+rather than a completely rigid sphere, the velocity inside the sphere
+is not uniform. The error bars indicate the variation in velocity
+across the sphere.
 
 
 .. fig:Error-in-velocity
@@ -104,3 +104,4 @@
    the error scaled with [;h;]. So the higher resolution
    errors are multiplied by 2, 4 and 8.
    
+.. |times| unicode:: U+00D7