[SCM] Gerris Flow Solver branch, upstream, updated. b3aa46814a06c9cb2912790b23916ffb44f1f203
Stephane Popinet
stephane.popinet at paradise.net.nz
Fri May 15 02:51:45 UTC 2009
The following commit has been merged in the upstream branch:
commit 5bbb5725b303d98581723b8b7d861be8be901b76
Author: Stephane Popinet <stephane.popinet at paradise.net.nz>
Date: Sun Apr 3 19:52:43 2005 +1000
New time-reversed VOF advection example
darcs-hash:20050403095243-fa380-ca0d7766bcf782cbd498405abea52f5d2a704b67.gz
diff --git a/doc/examples/Makefile.am b/doc/examples/Makefile.am
index 1965b71..f5b23a9 100644
--- a/doc/examples/Makefile.am
+++ b/doc/examples/Makefile.am
@@ -2,7 +2,8 @@
EXAMPLES = \
cylinder \
- lid
+ lid \
+ shear
EXTRA_DIST = \
template.tex \
diff --git a/doc/examples/shear/circle.gts b/doc/examples/shear/circle.gts
new file mode 100644
index 0000000..ac64f17
--- /dev/null
+++ b/doc/examples/shear/circle.gts
@@ -0,0 +1,6591 @@
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diff --git a/doc/examples/shear/shear.gfs b/doc/examples/shear/shear.gfs
new file mode 100644
index 0000000..d46a1e2
--- /dev/null
+++ b/doc/examples/shear/shear.gfs
@@ -0,0 +1,121 @@
+# Title: Time-reversed VOF advection in a shear flow
+#
+# Description:
+#
+# A test case initially presented by Rudman (Int. J. Num. Meth. Fluids, 1997).
+# A circular patch of tracer is advected in a vortical shear flow. At t = 2.5
+# the flow direction is reversed. An exact advection scheme would restore the
+# initial circular shape at t = 5.
+#
+# The VOF (Volume-Of-Fluid) advection scheme is not exact. The initial, intermediate
+# and final shape of the interface are represented on Figure \ref{advection}.
+# Figure \ref{error} illustrates the error between the initial and final shapes. The
+# corresponding error norms are given in Table \ref{norms}.
+#
+# \begin{figure}[htbp]
+# \begin{center}
+# \begin{tabular}{ccc}
+# \includegraphics[width=0.3\hsize]{t-0.eps} &
+# \includegraphics[width=0.3\hsize]{t-2.5.eps} &
+# \includegraphics[width=0.3\hsize]{t-5.eps} \\
+# (a) & (b) & (c)
+# \end{tabular}
+# \end{center}
+# \caption{Volume fraction field at times (a) 0, (b) 2.5 and (c) 5.}
+# \label{advection}
+# \end{figure}
+#
+# \begin{figure}[htbp]
+# \begin{center}
+# \includegraphics[width=0.4\hsize]{dt-5.eps}
+# \end{center}
+# \caption{Difference between the initial and final volume fraction field.}
+# \label{error}
+# \end{figure}
+#
+# \begin{table}[htbp]
+# \begin{center}
+# \begin{tabular}{lll}
+# $||^1$ & $||^2$ & $||^\infty$ \\
+# \input{norms.tex}
+# \end{tabular}
+# \end{center}
+# \caption{Norms of the error between the initial and final field.}
+# \label{norms}
+# \end{table}
+#
+# Author: St\'ephane Popinet
+# Command: gerris2D shear.gfs
+# Version: 0.6.4
+# Required files: circle.gts
+# Running time: 6 minutes
+# Generated files: t-0.eps t-2.5.eps t-5.eps dt-5.eps norms.tex
+#
+# The type of the simulation is GfsAdvection which only solves the advection
+# of passive tracers.
+1 0 GfsAdvection GfsBox GfsGEdge {} {
+ Time { end = 5 }
+ Refine 8
+
+ # Add tracer T, using a VOF advection scheme
+ VariableTracer {} T { scheme = vof }
+
+ # Initialize T as the volume fraction of each cell contained inside the
+ # volume defined by circle.gts
+ InitFraction {} T circle.gts
+
+ # Initialize U and V with the vortical shear flow field
+ Init {} {
+ U = {
+ x = (x + 0.5)*M_PI;
+ y = (y + 0.5)*M_PI;
+ return sin(x)*cos(y);
+ }
+ V = {
+ x = (x + 0.5)*M_PI;
+ y = (y + 0.5)*M_PI;
+ return -cos(x)*sin(y);
+ }
+ }
+
+ # At t = 2.5 re-initialize U and V with the reversed flow field
+ Init { start = 2.5 } {
+ U = {
+ x = (x + 0.5)*M_PI;
+ y = (y + 0.5)*M_PI;
+ return -sin(x)*cos(y);
+ }
+ V = {
+ x = (x + 0.5)*M_PI;
+ y = (y + 0.5)*M_PI;
+ return cos(x)*sin(y);
+ }
+ }
+
+ # Adapt the mesh dynamically so that at any time the maximum of the gradient
+ # of T is less than 1e-2 per cell length
+ AdaptGradient { istep = 1 } { cmax = 1e-2 maxlevel = 8 minlevel = 7 } T
+
+ # Output progress report on standard error
+ OutputProgress { istep = 1 } stderr
+
+ OutputPPM { start = 0 } { convert -colors 256 ppm:- t-0.eps } { v = T }
+ OutputPPM { start = 2.5 } { convert -colors 256 ppm:- t-2.5.eps } { v = T }
+ OutputPPM { start = 5 } { convert -colors 256 ppm:- t-5.eps } { v = T }
+
+ # Add a new variable
+ Variable {} Tref
+
+ # Initialize Tref with the initial shape
+ InitFraction { start = end } Tref circle.gts
+
+ # Output the norms of the difference between T and Tref, stores that into
+ # new variable DT
+ OutputErrorNorm { start = end } { awk '{print $5 " & " $7 " & " $9}' > norms.tex } { v = T } {
+ s = { return Tref; } v = DT
+ }
+
+ OutputPPM { start = end } { convert -colors 256 ppm:- dt-5.eps } { v = DT }
+ OutputTiming { start = end } stderr
+}
+GfsBox {}
diff --git a/doc/examples/template.tex b/doc/examples/template.tex
index 4e0378a..3a0780d 100644
--- a/doc/examples/template.tex
+++ b/doc/examples/template.tex
@@ -42,6 +42,7 @@ The usefulness and quality of this document very much depend on the contribution
\input{cylinder/cylinder.tex}
\input{cylinder/heated/heated.tex}
\input{lid/lid.tex}
+\input{shear/shear.tex}
\section{How to write examples}
\label{howto}
--
Gerris Flow Solver
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