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# Title: Dam break on complex topography
#
# Description:
#
# An example similar to that
# \htmladdnormallinkfoot{presented}{http://www.amath.washington.edu/~rjl/catalina/leveque1.pdf}
# by Randall J. LeVeque illustrating the solution of the
# \htmladdnormallinkfoot{Saint-Venant}{http://en.wikipedia.org/wiki/Shallow\_water\_equations}
# (or shallow-water) equations with complex topography, wetting and
# drying, shocks and hydrostatic equilibrium.
#
# \begin{figure}[htbp]
# \caption{Topography (red) and animation of the water level (blue).}
# \begin{rawhtml}
# <DIV CLASS="center">
# <IMG SRC="dam/dam.gif">
# </DIV>
# \end{rawhtml}
# \end{figure}
#
# Author: St\'ephane Popinet
# Command: gerris2D dam.gfs
# Version: 1.3.1
# Required files: dam.plot
# Running time: 2 minutes
# Generated files: dam.gif
#
# Use the GfsRiver Saint-Venant solver
1 0 GfsRiver GfsBox GfsGEdge {} {
PhysicalParams { L = 8. }
# Define a 1D domain using cell masking
RefineSurface 9 (y - 8.*(0.5 - 1./512.))
InitMask {} (y < 8.*(0.5 - 1./512.))
# Set the topography Zb and the initial water surface elevation P
Init {} {
Zb = x*x/8.+cos(M_PI*x)/2.
P = {
double p = x > 0. ? 0.35 : x < -2. ? 1.9 : -1.;
return MAX (0., p - Zb);
}
}
PhysicalParams { g = 1. }
# Use a first-order scheme rather than the default second-order
# minmod limiter. This is just to add some numerical damping.
AdvectionParams {
# gradient = gfs_center_minmod_gradient
gradient = none
}
Time { end = 40 }
OutputProgress { istep = 10 } stderr
OutputScalarSum { istep = 10 } ke { v = (P > 0. ? U*U/P : 0.) }
OutputScalarSum { istep = 10 } vol { v = P }
OutputScalarNorm { istep = 10 } u { v = (P > 0. ? U/P : 0.) }
# use gfsplot/gnuplot for online visualisation and generation of figures
OutputSimulation { step = 0.3 } {
gfsplot "
load 'dam.plot'
set title sprintf('t = %4.1f', (t))
plot [-4.:4.]'-' u (x):(Zb):(H) w filledcu lc 3, \
'-' u (x):(Zb) w l lw 4 lc 1 lt 1
set term pngcairo size 800,600
set output sprintf('sim-%04.1f.png', (t))
replot
set term wxt noraise
"
} { format = text }
# Combine all the gif images into a gif animation using gifsicle
EventScript { start = end } {
echo "\rcreating animation... " > /dev/stderr
sleep 10 # give a chance to gnuplot to catch up
for f in sim-*.png; do
convert $f -trim +repage -bordercolor white \
-border 10 -resize 640x282! `basename $f .png`.gif && rm -f $f
done
gifsicle --colors 256 --optimize --delay 12 --loopcount=0 sim-*.gif > dam.gif && \
rm -f sim-*.gif
}
}
GfsBox {
left = Boundary
right = Boundary
}
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