[SCM] Gerris Flow Solver branch, upstream, updated. b3aa46814a06c9cb2912790b23916ffb44f1f203

Stephane Popinet s.popinet at niwa.co.nz
Fri May 15 02:52:02 UTC 2009


The following commit has been merged in the upstream branch:
commit d18231a93859d0d3056e9dab78996235f6ef173e
Author: Stephane Popinet <s.popinet at niwa.co.nz>
Date:   Fri Jun 17 10:44:24 2005 +1000

    New 4-way vortex merging test case
    
    darcs-hash:20050617004424-fbd8f-a101f022135e80b0a2275a73364d5a1464856c9f.gz

diff --git a/test/euler/Makefile.am b/test/euler/Makefile.am
index fb909da..ca7f1e5 100644
--- a/test/euler/Makefile.am
+++ b/test/euler/Makefile.am
@@ -2,7 +2,8 @@
 
 TESTDIRS = \
 	reynolds \
-	periodic
+	periodic \
+	merging
 
 EXTRA_DIST = \
 	template.tex \
diff --git a/doc/examples/boussinesq/boussinesq.gfv b/test/euler/merging/levels.gfv
similarity index 54%
copy from doc/examples/boussinesq/boussinesq.gfv
copy to test/euler/merging/levels.gfv
index 2d4657f..84f69dd 100644
--- a/doc/examples/boussinesq/boussinesq.gfv
+++ b/test/euler/merging/levels.gfv
@@ -1,22 +1,20 @@
 # GfsView 2D
 View {
-  tx = -0.00447772 ty = -0.419694
+  tx = 0 ty = 0
   q0 = 0 q1 = 0 q2 = 0 q3 = 1
-  zoom = -21.0352
+  zoom = -11.6434
   r = 0.3 g = 0.4 b = 0.6
   res = 1
   lc = 0.001
   reactivity = 0.1
 }
-Linear {
+Boundaries {
+  r = 0 g = 0 b = 0
+  shading = Constant
+  maxlevel = 8
+}
+Levels {
   r = 0 g = 0 b = 0
   shading = Constant
   maxlevel = 8
-} {
-  v = T
-  amin = 0 min = 1.9696e-19
-  amax = 0 max = 1
-  cmap = Jet
-} {
-  scale = 0
 }
diff --git a/test/euler/merging/merging.gfs b/test/euler/merging/merging.gfs
new file mode 100644
index 0000000..d091444
--- /dev/null
+++ b/test/euler/merging/merging.gfs
@@ -0,0 +1,158 @@
+# Title: Convergence for the three-way vortex merging problem
+#
+# Description:
+#
+# Another of the test cases presented in Popinet \cite{popinet2003},
+# initially used by Almgren et al. \cite{almgren98}, this convergence
+# test illustrates the second-order accuracy of Gerris when refinement
+# is placed appropriately, either through static refinement or dynamic
+# adaptive refinement.
+#
+# Four vortices are placed in the unit-square, centred at $(0,0)$,
+# $(0.09,0)$, $(-0.045,0.045\sqrt{3})$ and $(-0.045,$ $-0.045\sqrt{3})$
+# and of strengths $-150$, $50$, $50$, $50$ respectively. The profile of
+# each vortex centred around $(x_i,y_i)$ is
+# $$
+# {1+\tanh(100(0.03-r_i))\over 2},
+# $$
+# where $r_i=\sqrt{(x-x_i)^2+(y-y_i)^2}$. To initialise the velocity
+# field, we use this vorticity as the source term in the Poisson
+# equation for the streamfunction $\psi$
+# $$
+# \nabla^2\psi=\|\nabla\times{\bf U}\|.
+# $$
+# Each component of the velocity field is then calculated from the
+# streamfunction. No-flow boundary conditions are used on the four sides
+# of the domain and the simulations are ran to $t=0.25$ using a CFL of
+# 0.9.
+#
+# Two different discretisations are used, each time with up to $L$
+# levels of refinement: a grid using static refinement in concentric
+# circles of decreasing radius and a grid using dynamic adaptive
+# refinement. The ``circle'' grid is constructed by starting from a
+# uniform grid with four levels of refinement and by successively adding
+# one level to all the cells contained within circles centred on the
+# origin and of radii:
+# \begin{itemize}
+# \item $L=6$: 0.25, 0.15
+# \item $L=7$: 0.25, 0.2, 0.15
+# \item $L=8$: 0.25, 0.2, 0.175, 0.15
+# \item $L=9$: 0.25, 0.2, 0.175, 0.1625, 0.15
+# \end{itemize}
+# For the dynamically refined grid, the vorticity-based criterion is
+# applied at every timestep with a threshold $\tau=4\times10^{-3}$. As
+# we do not have an analytical solution for this problem, Richardson
+# extrapolation is used.
+#
+# Figure \ref{vorticity} illustrates the evolution of the vorticity
+# and of the adaptively refined grid for $L=8$. The most refined level
+# closely follows the three outer vortices as they orbit the central
+# one. Far from the vortices, a very coarse mesh is used ($l=3$). One
+# may note a few isolated patches of refinement scattered at the
+# periphery of the outer vortices. They are due to the numerical noise
+# added to the vorticity by the interpolation procedure necessary to
+# fill in velocity values for newly created cells. This could be
+# improved by using higher-order interpolants.
+#
+# Table \ref{convergence} summarises the results obtained for the
+# first twelve calculations. For fine enough grids close to
+# second-order convergence is obtained for both norms and for the two
+# discretisations used. The norms of the error on the various grids
+# are also comparable for a given resolution, but fine adaptive meshes
+# show a degradation in convergence due to the numerical noise.
+#
+# \begin{table}
+# \begin{center}
+# \input{convergence.tex}
+# \end{center}
+# \caption{Errors and convergence orders in the $x$-component of the
+# velocity for the four-way vortex merging problem. The reference
+# solution values are given in blue.}
+# \label{convergence}
+# \end{table}
+#
+# \begin{figure}
+# \begin{center}
+# \begin{tabular}{cc}
+# \includegraphics*[width=0.3\hsize]{tv_0_05.eps} &
+# \includegraphics*[width=0.3\hsize]{tm_0_05.eps} \\
+# \multicolumn{2}{c}{$t=0.05$} \\
+# \\
+# \includegraphics*[width=0.3\hsize]{tv_0_15.eps} &
+# \includegraphics*[width=0.3\hsize]{tm_0_15.eps} \\
+# \multicolumn{2}{c}{$t=0.15$} \\
+# \\
+# \includegraphics*[width=0.3\hsize]{tv_0_25.eps} &
+# \includegraphics*[width=0.3\hsize]{tm_0_25.eps} \\
+# \multicolumn{2}{c}{$t=0.25$}
+# \end{tabular}
+# \end{center}
+# \caption{Contour plots of vorticity (left) and adaptive grids used
+# (right) for the four-way vortex merging calculation. The lines on the
+# pictures in the right column represent the boundaries between levels
+# of refinement (with a maximum of $L=8$ levels).}
+# \label{vorticity}
+# \end{figure}
+#
+# Author: St\'ephane Popinet
+# Command: sh merging.sh merging.gfs
+# Version: 0.6.4
+# Required files: merging.sh levels.gfv vorticity.gfv sim.err.ref simc.err.ref
+# Running time: 3 minutes
+# Generated files: convergence.tex tv_0_05.eps tm_0_05.eps tv_0_15.eps tm_0_15.eps tv_0_25.eps tm_0_25.eps
+#
+1 0 GfsSimulation GfsBox GfsGEdge {} {
+  Time { end = 0.3 }
+  AdvectionParams { cfl = 0.9 }
+  ApproxProjectionParams { tolerance = 1e-5 }
+  ProjectionParams { tolerance = 1e-5 }
+  Refine {
+    double r = sqrt(x*x + y*y);
+    switch (LEVEL) {
+    case 6: return r > 0.25 ? 4 : r > 0.15 ? 5 : 6;
+    case 7: return r > 0.25 ? 4 : r > 0.2 ? 5 : r > 0.15 ? 6 : 7;
+    case 8: return r > 0.25 ? 4 : r > 0.2 ? 5 : r > 0.175 ? 6 : r > 0.15 ? 7 : 8;
+    case 9: return r > 0.25 ? 4 : r > 0.2 ? 5 : r > 0.175 ? 6 : r > 0.1625 ? 7 : r > 0.15 ? 8 : 9;
+    }
+  }
+  InitVorticity {} {
+    double vortex (double xo, double yo, double s) {
+      double r = sqrt ((x - xo)*(x - xo) + (y - yo)*(y - yo));
+      return s*(1. + tanh (100.*(0.03 - r)))/2.;
+    }
+    return vortex (0., 0., -150.) + 
+           vortex (0.09, 0., 50.) + 
+           vortex (-0.045, 0.0779422863406, 50.) +
+           vortex (-0.045, -0.0779422863406, 50.);
+  }
+  AdaptVorticity { istep = 1 } { maxlevel = LEVEL cmax = 4e-3 }
+  OutputSimulation { start = 0.05 } stdout {}
+  EventScript { start = 0.05 } {
+    echo Clear
+    cat levels.gfv
+    echo Save tm_0_05.eps { format = EPS line_width = 0.1 }
+    echo Clear
+    cat vorticity.gfv
+    echo Save tv_0_05.eps { format = EPS line_width = 0.1 }
+  }
+  OutputSimulation { start = 0.15 } stdout {}
+  EventScript { start = 0.15 } {
+    echo Clear
+    cat levels.gfv
+    echo Save tm_0_15.eps { format = EPS line_width = 0.1 }
+    echo Clear
+    cat vorticity.gfv
+    echo Save tv_0_15.eps { format = EPS line_width = 0.1 }
+  }
+  OutputSimulation { start = 0.25 } stdout {}
+  EventScript { start = 0.25 } {
+    echo Clear
+    cat levels.gfv
+    echo Save tm_0_25.eps { format = EPS line_width = 0.1 }
+    echo Clear
+    cat vorticity.gfv
+    echo Save tv_0_25.eps { format = EPS line_width = 0.1 }
+  }
+  OutputSimulation { start = 0.25 } SIM {}
+}
+GfsBox {}
diff --git a/test/euler/merging/merging.sh b/test/euler/merging/merging.sh
new file mode 100644
index 0000000..e2ba918
--- /dev/null
+++ b/test/euler/merging/merging.sh
@@ -0,0 +1,90 @@
+if ! $donotrun; then
+    if sed "s/LEVEL/8/g" < $1 | \
+       sed "s/SIM/sim-8/g" | \
+       gerris2D - | gfsview2D; then :
+    else
+	exit 1
+    fi
+
+    for level in 6 7 9; do
+	if sed "s/LEVEL/$level/g" < $1 | \
+           sed "s/SIM/sim-$level/g" | \
+           gerris2D - > /dev/null; then :
+	else
+	    exit 1
+	fi
+    done
+
+    for level in 6 7 8 9; do
+	if sed "s/LEVEL/$level/g" < $1 | \
+           sed "s/AdaptVorticity/# AdaptVorticity/g" | \
+           sed "s/SIM/simc-$level/g" | \
+           gerris2D - > /dev/null; then :
+	else
+	    exit 1
+	fi
+    done
+fi
+
+for s in sim simc; do
+    rm -f $s.err
+    for level in 6 7 8; do
+	level1=`expr $level + 1`
+	echo -n "$level " >> $s.err
+	if gfscompare2D -v $s-$level $s-$level1 U 2>&1 | \
+	    awk '{if ($1 == "total") print $6 " " $8;}' >> $s.err; then :
+	else
+	    exit 1
+	fi
+    done
+done
+
+if cat <<EOF | python > convergence.tex ; then :
+from check import *
+from sys import *
+from math import *
+
+print r"""\begin{tabular}{|c|c|c|c|c|c|}\hline
+Domain   & \multicolumn{5}{c|}{\$L_2\$}\\\ \hline
+         & \$L=6\$   & \$O_2\$ & \$L=7\$    & \$O_2\$ & \$L=8\$  \\\ \hline"""
+
+def order(r,color='black'):
+   for i in range(0,len(r.l)-1):
+     y0,y1 = r.l[i][1],r.l[i+1][1]
+     print '& {\color{%s}%.2e} & {\color{%s}%4.2f}' % (color, y0, color, log(y0/y1)/log(2.)),
+   print '& {\color{%s}%.2e}' % (color, r.l[i+1][1]), r'\\\'
+
+print 'Circle',
+order(Curve('simc.err',1,2))
+order(Curve('simc.err',1,2), 'blue')
+print 'Adaptive',
+order(Curve('sim.err',1,2))
+order(Curve('sim.err',1,2), 'blue')
+
+print r"""\hline
+Domain   & \multicolumn{5}{c|}{\$L_\infty\$} \\\ \hline
+         &  \$L=6\$   & \$O_\infty\$ & \$L=7\$   & \$O_\infty\$ & \$L=8\$ \\\ \hline"""
+
+print 'Circle',
+order(Curve('simc.err',1,3))
+order(Curve('simc.err',1,3), 'blue')
+print 'Adaptive',
+order(Curve('sim.err',1,3))
+order(Curve('sim.err',1,3), 'blue')
+
+print r"\hline\end{tabular}"
+EOF
+else
+    exit 1
+fi
+
+if cat <<EOF | python ; then :
+from check import *
+from sys import *
+if (Curve('sim.err',1,2) - Curve('sim.err.ref',1,2)).max() > 1e-6 or\
+   (Curve('simc.err',1,3) - Curve('simc.err.ref',1,3)).max() > 1e-6:
+  exit(1)
+EOF
+else
+   exit 1
+fi
diff --git a/test/euler/merging/sim.err.ref b/test/euler/merging/sim.err.ref
new file mode 100644
index 0000000..4e826e3
--- /dev/null
+++ b/test/euler/merging/sim.err.ref
@@ -0,0 +1,4 @@
+6 2.581e-02 4.400e-01
+7 1.084e-02 1.888e-01
+8 3.357e-03 4.862e-02
+9 2.073e-03 2.560e-02
diff --git a/test/euler/merging/simc.err.ref b/test/euler/merging/simc.err.ref
new file mode 100644
index 0000000..a8d83b7
--- /dev/null
+++ b/test/euler/merging/simc.err.ref
@@ -0,0 +1,4 @@
+6 2.599e-02 4.470e-01
+7 1.043e-02 1.861e-01
+8 2.674e-03 4.852e-02
+9 6.892e-04 1.322e-02
diff --git a/doc/examples/boussinesq/boussinesq.gfv b/test/euler/merging/vorticity.gfv
similarity index 55%
copy from doc/examples/boussinesq/boussinesq.gfv
copy to test/euler/merging/vorticity.gfv
index 2d4657f..475e5ac 100644
--- a/doc/examples/boussinesq/boussinesq.gfv
+++ b/test/euler/merging/vorticity.gfv
@@ -1,22 +1,27 @@
 # GfsView 2D
 View {
-  tx = -0.00447772 ty = -0.419694
+  tx = 0 ty = 0
   q0 = 0 q1 = 0 q2 = 0 q3 = 1
-  zoom = -21.0352
+  zoom = -11.6434
   r = 0.3 g = 0.4 b = 0.6
   res = 1
   lc = 0.001
   reactivity = 0.1
 }
-Linear {
+Isoline {
   r = 0 g = 0 b = 0
   shading = Constant
   maxlevel = 8
 } {
-  v = T
-  amin = 0 min = 1.9696e-19
-  amax = 0 max = 1
+  v = Vorticity
+  amin = 1
+  amax = 1
   cmap = Jet
 } {
-  scale = 0
+  n = 17
+}
+Boundaries {
+  r = 0 g = 0 b = 0
+  shading = Constant
+  maxlevel = 8
 }
diff --git a/test/euler/periodic/periodic.sh b/test/euler/periodic/periodic.sh
index e73d07c..64b91f5 100644
--- a/test/euler/periodic/periodic.sh
+++ b/test/euler/periodic/periodic.sh
@@ -25,33 +25,37 @@ print r"""\begin{tabular}{|c|c|c|c|c|c|}\hline
         & \multicolumn{5}{c|}{\$L_2\$} \\\ \hline
         & \$L=5\$   & \$O_2\$ & \$L=6\$    & \$O_2\$ & \$L=7\$  \\\ \hline"""
 
-def order(r,rr):
+def order(r,color='black'):
    for i in range(0,len(r.l)-1):
      y0,y1 = r.l[i][1],r.l[i+1][1]
-     yr0,yr1 = rr.l[i][1],rr.l[i+1][1]
-     print '& %.2e / {\color{blue}%.2e} & %4.2f / {\color{blue}%4.2f}' % \
-       (y0, yr0, log(y0/y1)/log(2.), log(yr0/yr1)/log(2.)),
-   print '& %.2e / {\color{blue}%.2e}' % (r.l[i+1][1],rr.l[i+1][1]), r'\\\ \hline'
+     print '& {\color{%s}%.2e} & {\color{%s}%4.2f}' % (color, y0, color, log(y0/y1)/log(2.)),
+   print '& {\color{%s}%.2e}' % (color, r.l[i+1][1]), r'\\\'
 
 print 'Uniform',
-order(Curve('r0',1,2),Curve('r0.ref',1,2))
+order(Curve('r0',1,2))
+order(Curve('r0.ref',1,2),'blue')
 print '\$r=1\$',
-order(Curve('r1',1,2),Curve('r1.ref',1,2))
+order(Curve('r1',1,2))
+order(Curve('r1.ref',1,2),'blue')
 print '\$r=2\$',
-order(Curve('r2',1,2),Curve('r2.ref',1,2))
+order(Curve('r2',1,2))
+order(Curve('r2.ref',1,2),'blue')
 
 print r"""\hline
         & \multicolumn{5}{c|}{\$L_\infty\$} \\\ \hline
         & \$L=5\$   & \$O_\infty\$  & \$L=6\$   & \$O_\infty\$  & \$L=7\$ \\\ \hline"""
 
 print 'Uniform',
-order(Curve('r0',1,3),Curve('r0.ref',1,3))
+order(Curve('r0',1,3))
+order(Curve('r0.ref',1,3),'blue')
 print '\$r=1\$',
-order(Curve('r1',1,3),Curve('r1.ref',1,3))
+order(Curve('r1',1,3))
+order(Curve('r1.ref',1,3),'blue')
 print '\$r=2\$',
-order(Curve('r2',1,3),Curve('r2.ref',1,3))
+order(Curve('r2',1,3))
+order(Curve('r2.ref',1,3),'blue')
 
-print r'\end{tabular}'
+print r"\hline\end{tabular}"
 EOF
 else
     exit 1
diff --git a/test/euler/reference2D/merging.xmgr b/test/euler/reference2D/merging.xmgr
deleted file mode 100644
index 5b2a132..0000000
--- a/test/euler/reference2D/merging.xmgr
+++ /dev/null
@@ -1,2012 +0,0 @@
-# ACE/gr parameter file
-#
- at version 40102
- at page layout free
- at ps linewidth begin 1
- at ps linewidth increment 2
- at hardcopy device 1
- at description "merging.sh"
- at page 5
- at page inout 5
- at link page off
- at default linestyle 1
- at default linewidth 1
- at default color 1
- at default char size 1.000000
- at default font 4
- at default font source 0
- at default symbol size 1.000000
- at timestamp off
- at timestamp 0.03, 0.03
- at timestamp linewidth 1
- at timestamp color 1
- at timestamp rot 0
- at timestamp font 4
- at timestamp char size 1.000000
- at timestamp def "Tue Jun  4 04:38:48 2002"
- at with g0
- at g0 on
- at g0 label off
- at g0 hidden false
- at g0 type logy
- at g0 autoscale type AUTO
- at g0 fixedpoint off
- at g0 fixedpoint type 0
- at g0 fixedpoint xy 0.000000, 0.000000
- at g0 fixedpoint format general general
- at g0 fixedpoint prec 6, 6
-@    world xmin 0
-@    world xmax 4
-@    world ymin 1e-07
-@    world ymax 0.01
-@    stack world 0, 0, 0, 0 tick 0, 0, 0, 0
-@    view xmin 0.100000
-@    view xmax 0.475000
-@    view ymin 0.100000
-@    view ymax 0.475000
-@    title ""
-@    title font 4
-@    title size 1.500000
-@    title color 1
-@    title linewidth 1
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-@    subtitle size 1.000000
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-@    s0 fill pattern 0
-@    s0 errorbar type BOTH
-@    s0 errorbar length 1.000000
-@    s0 errorbar linewidth 1
-@    s0 errorbar linestyle 1
-@    s0 errorbar riser on
-@    s0 errorbar riser linewidth 1
-@    s0 errorbar riser linestyle 1
-@    s0 xyz 0.000000, 0.000000
-@    s0 comment "/tmp/toto"
-@    s1 symbol 3
-@    s1 symbol size 0.440000
-@    s1 symbol fill 2
-@    s1 symbol color 1
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-@    s1 errorbar type BOTH
-@    s1 errorbar length 1.000000
-@    s1 errorbar linewidth 1
-@    s1 errorbar linestyle 1
-@    s1 errorbar riser on
-@    s1 errorbar riser linewidth 1
-@    s1 errorbar riser linestyle 1
-@    s1 xyz 0.000000, 0.000000
-@    s1 comment "reference/time.xmgr"
-@    s2 symbol 5
-@    s2 symbol size 0.340000
-@    s2 symbol fill 2
-@    s2 symbol color 1
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-@    s2 symbol linestyle 1
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-@    s2 errorbar type BOTH
-@    s2 errorbar length 1.000000
-@    s2 errorbar linewidth 1
-@    s2 errorbar linestyle 1
-@    s2 errorbar riser on
-@    s2 errorbar riser linewidth 1
-@    s2 errorbar riser linestyle 1
-@    s2 xyz 0.000000, 0.000000
-@    s2 comment "reference/time.xmgr"
-@    s3 symbol 2
-@    s3 symbol size 0.340000
-@    s3 symbol fill 1
-@    s3 symbol color 1
-@    s3 symbol linewidth 1
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-@    s3 errorbar type BOTH
-@    s3 errorbar length 1.000000
-@    s3 errorbar linewidth 1
-@    s3 errorbar linestyle 1
-@    s3 errorbar riser on
-@    s3 errorbar riser linewidth 1
-@    s3 errorbar riser linestyle 1
-@    s3 xyz 0.000000, 0.000000
-@    s3 comment "/tmp/toto.xmgr"
-@    s4 symbol 3
-@    s4 symbol size 0.440000
-@    s4 symbol fill 1
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- at WITH G0
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- at TARGET S0
- at TYPE xy
-             0.2      2.21978e-06
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-&
- at TARGET S1
- at TYPE xy
-             0.2      4.33583e-06
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-&
- at TARGET S2
- at TYPE xy
-             0.2       4.2125e-05
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-&
- at TARGET S3
- at TYPE xy
-             0.2      8.83404e-07
-             0.4      1.01738e-06
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-             3.8        5.884e-06
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-&
- at TARGET S4
- at TYPE xy
-             0.2      1.56981e-06
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-&
- at TARGET S5
- at TYPE xy
-             0.2        2.395e-05
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-&
- at WITH G1
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- at TYPE xy
-             0.2      5.66345e-06
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-&
- at TARGET S1
- at TYPE xy
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-&
- at TARGET S2
- at TYPE xy
-             0.2      3.14675e-05
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-&
- at TARGET S3
- at TYPE xy
-             0.2      1.39628e-06
-             0.4      1.63765e-06
-             0.6       2.0245e-06
-             0.8      2.34904e-06
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-             3.6      1.31465e-05
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-&
- at TARGET S4
- at TYPE xy
-             0.2      1.93514e-06
-             0.4      2.27903e-06
-             0.6      2.77608e-06
-             0.8      3.42825e-06
-               1      4.62756e-06
-             1.2      5.86099e-06
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-&
- at TARGET S5
- at TYPE xy
-             0.2         1.26e-05
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-&
- at WITH G2
- at G2 ON
- at TARGET S0
- at TYPE xy
-             0.2          1.32927
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-             1.2           1.4946
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-&
- at TARGET S1
- at TYPE xy
-             0.2          1.46572
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-&
- at TARGET S2
- at TYPE xy
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-             3.4          1.50677
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-&
- at WITH G3
- at G3 ON
- at TARGET S0
- at TYPE xy
-             0.2          2.02009
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-             3.2          2.20086
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-&
- at TARGET S1
- at TYPE xy
-             0.2          1.99018
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-             3.2           2.0351
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-&
- at TARGET S2
- at TYPE xy
-             0.2          1.32044
-             0.4          1.42523
-             0.6          1.78608
-             0.8           2.0187
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-               3          1.66023
-             3.2          1.59979
-             3.4          1.50677
-             3.6          1.55319
-             3.8          1.92172
-               4          1.73332
-&
diff --git a/test/euler/reference2D/merging_convective.xmgr b/test/euler/reference2D/merging_convective.xmgr
deleted file mode 100644
index f6cac53..0000000
--- a/test/euler/reference2D/merging_convective.xmgr
+++ /dev/null
@@ -1,2012 +0,0 @@
-# ACE/gr parameter file
-#
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-@    legend box off
-@    legend box fill off
-@    legend box fill with color
-@    legend box fill color 0
-@    legend box fill pattern 1
-@    legend box color 1
-@    legend box linewidth 1
-@    legend box linestyle 1
-@    legend x1 0.61
-@    legend y1 0.75
-@    legend font 4
-@    legend char size 0.450000
-@    legend linestyle 1
-@    legend linewidth 1
-@    legend color 1
-@    legend string 0 "L1 norm"
-@    legend string 1 "L2 norm"
-@    legend string 2 "Lmax norm"
-@    frame on
-@    frame type 0
-@    frame linestyle 1
-@    frame linewidth 1
-@    frame color 1
-@    frame fill off
-@    frame background color 0
- at WITH G0
- at G0 ON
- at TARGET S0
- at TYPE xy
-             0.2      2.24464e-06
-             0.4      2.54715e-06
-             0.6      2.91755e-06
-             0.8      3.40125e-06
-               1       4.2403e-06
-             1.2      5.10047e-06
-             1.4      5.87334e-06
-             1.6      6.61043e-06
-             1.8      7.47984e-06
-               2      8.56823e-06
-             2.2      9.95289e-06
-             2.4      1.11785e-05
-             2.6       1.2046e-05
-             2.8      1.20422e-05
-               3      1.16794e-05
-             3.2      1.25275e-05
-             3.4      1.37091e-05
-             3.6      1.48164e-05
-             3.8      1.58382e-05
-               4       1.6839e-05
-&
- at TARGET S1
- at TYPE xy
-             0.2      4.37876e-06
-             0.4       5.0728e-06
-             0.6      6.03474e-06
-             0.8      7.96343e-06
-               1      1.08944e-05
-             1.2      1.41565e-05
-             1.4      1.75026e-05
-             1.6      2.09852e-05
-             1.8      2.47036e-05
-               2      2.92038e-05
-             2.2      3.40377e-05
-             2.4      3.77604e-05
-             2.6      3.91316e-05
-             2.8      3.81071e-05
-               3      3.67982e-05
-             3.2      3.81211e-05
-             3.4      4.24514e-05
-             3.6      4.99035e-05
-             3.8      5.82658e-05
-               4      6.66357e-05
-&
- at TARGET S2
- at TYPE xy
-             0.2        4.225e-05
-             0.4       3.8625e-05
-             0.6         4.41e-05
-             0.8      6.57025e-05
-               1        9.905e-05
-             1.2        0.0001482
-             1.4       0.00019985
-             1.6       0.00024995
-             1.8      0.000314782
-               2       0.00038361
-             2.2      0.000433415
-             2.4      0.000452425
-             2.6      0.000494435
-             2.8      0.000538525
-               3        0.0005035
-             3.2       0.00046455
-             3.4      0.000371362
-             3.6      0.000539503
-             3.8       0.00080345
-               4        0.0009609
-&
- at TARGET S3
- at TYPE xy
-             0.2       8.8695e-07
-             0.4      1.02507e-06
-             0.6      1.22693e-06
-             0.8      1.21179e-06
-               1      1.49837e-06
-             1.2      1.77233e-06
-             1.4      1.98568e-06
-             1.6      2.18414e-06
-             1.8      2.43879e-06
-               2      2.84009e-06
-             2.2      3.32623e-06
-             2.4      3.83008e-06
-             2.6      4.14927e-06
-             2.8      4.16516e-06
-               3      4.06948e-06
-             3.2      4.29842e-06
-             3.4       4.8195e-06
-             3.6      5.33456e-06
-             3.8      5.80838e-06
-               4      6.28809e-06
-&
- at TARGET S4
- at TYPE xy
-             0.2      1.57713e-06
-             0.4       1.7267e-06
-             0.6      2.00169e-06
-             0.8      2.31854e-06
-               1      3.02487e-06
-             1.2      3.74607e-06
-             1.4      4.43252e-06
-             1.6      5.16051e-06
-             1.8      5.97997e-06
-               2      7.40811e-06
-             2.2      9.31699e-06
-             2.4      1.09978e-05
-             2.6      1.19604e-05
-             2.8      1.18675e-05
-               3      1.16384e-05
-             3.2       1.1768e-05
-             3.4       1.2692e-05
-             3.6      1.47481e-05
-             3.8      1.74792e-05
-               4      2.04936e-05
-&
- at TARGET S5
- at TYPE xy
-             0.2       2.3925e-05
-             0.4         2.03e-05
-             0.6         1.51e-05
-             0.8       1.6155e-05
-               1       2.1875e-05
-             1.2       2.9525e-05
-             1.4         4.15e-05
-             1.6       5.3475e-05
-             1.8       6.6005e-05
-               2       8.4585e-05
-             2.2       0.00010431
-             2.4      0.000122588
-             2.6      0.000147342
-             2.8      0.000155937
-               3      0.000165425
-             3.2      0.000160975
-             3.4        0.0001336
-             3.6       0.00018231
-             3.8      0.000211562
-               4       0.00028432
-&
- at WITH G1
- at G1 ON
- at TARGET S0
- at TYPE xy
-             0.2      5.76335e-06
-             0.4      6.89323e-06
-             0.6      8.23469e-06
-             0.8      1.06251e-05
-               1      1.39928e-05
-             1.2      1.74256e-05
-             1.4      2.04866e-05
-             1.6      2.34152e-05
-             1.8      2.69165e-05
-               2      3.14178e-05
-             2.2      3.71661e-05
-             2.4      4.21991e-05
-             2.6      4.57699e-05
-             2.8      4.58114e-05
-               3      4.44101e-05
-             3.2      4.82042e-05
-             3.4      5.34525e-05
-             3.6      5.83842e-05
-             3.8      6.28809e-05
-               4      6.71901e-05
-&
- at TARGET S1
- at TYPE xy
-             0.2      7.78799e-06
-             0.4      9.51129e-06
-             0.6      1.16778e-05
-             0.8      1.58834e-05
-               1      2.20538e-05
-             1.2      2.88549e-05
-             1.4      3.58017e-05
-             1.6      4.30202e-05
-             1.8       5.0717e-05
-               2      6.00272e-05
-             2.2      7.00221e-05
-             2.4      7.77165e-05
-             2.6      8.05484e-05
-             2.8       7.8432e-05
-               3      7.57357e-05
-             3.2      7.84942e-05
-             3.4      8.74741e-05
-             3.6      0.000102897
-             3.8      0.000120185
-               4      0.000137477
-&
- at TARGET S2
- at TYPE xy
-             0.2       3.1144e-05
-             0.4      3.78525e-05
-             0.6         4.41e-05
-             0.8      6.57025e-05
-               1        9.905e-05
-             1.2        0.0001482
-             1.4       0.00019985
-             1.6       0.00024995
-             1.8      0.000314782
-               2       0.00038361
-             2.2      0.000433415
-             2.4      0.000452425
-             2.6      0.000494435
-             2.8      0.000538525
-               3        0.0005035
-             3.2       0.00046455
-             3.4      0.000371362
-             3.6      0.000539503
-             3.8       0.00080345
-               4        0.0009609
-&
- at TARGET S3
- at TYPE xy
-             0.2       1.4083e-06
-             0.4      1.66226e-06
-             0.6       2.0745e-06
-             0.8      2.40641e-06
-               1      3.10927e-06
-             1.2      3.78323e-06
-             1.4      4.30519e-06
-             1.6      4.78125e-06
-             1.8      5.41833e-06
-               2      6.43568e-06
-             2.2      7.66682e-06
-             2.4      8.94068e-06
-             2.6      9.76742e-06
-             2.8      9.80112e-06
-               3      9.56216e-06
-             3.2      1.01777e-05
-             3.4       1.1569e-05
-             3.6       1.2954e-05
-             3.8      1.42209e-05
-               4      1.54715e-05
-&
- at TARGET S4
- at TYPE xy
-             0.2      1.95389e-06
-             0.4      2.31717e-06
-             0.6       2.8443e-06
-             0.8      3.54121e-06
-               1      4.73713e-06
-             1.2      5.93199e-06
-             1.4      7.05919e-06
-             1.6      8.24821e-06
-             1.8      9.58377e-06
-               2      1.19058e-05
-             2.2      1.50031e-05
-             2.4      1.77269e-05
-             2.6      1.92866e-05
-             2.8      1.91363e-05
-               3      1.87665e-05
-             3.2      1.89786e-05
-             3.4      2.04785e-05
-             3.6      2.38106e-05
-             3.8      2.82326e-05
-               4      3.31103e-05
-&
- at TARGET S5
- at TYPE xy
-             0.2         1.25e-05
-             0.4         1.41e-05
-             0.6         1.27e-05
-             0.8       1.6155e-05
-               1       2.1875e-05
-             1.2       2.9525e-05
-             1.4         4.15e-05
-             1.6       5.3475e-05
-             1.8       6.6005e-05
-               2       8.4585e-05
-             2.2       0.00010431
-             2.4      0.000122588
-             2.6      0.000147342
-             2.8      0.000155937
-               3      0.000165425
-             3.2      0.000160975
-             3.4        0.0001336
-             3.6       0.00018231
-             3.8      0.000211562
-               4       0.00028432
-&
- at WITH G2
- at G2 ON
- at TARGET S0
- at TYPE xy
-             0.2          1.33956
-             0.4          1.31316
-             0.6           1.2497
-             0.8          1.48893
-               1          1.50077
-             1.2          1.52498
-             1.4          1.56455
-             1.6          1.59768
-             1.8          1.61684
-               2          1.59306
-             2.2          1.58123
-             2.4          1.54528
-             2.6          1.53762
-             2.8          1.53166
-               3          1.52105
-             3.2          1.54322
-             3.4          1.50818
-             3.6          1.47375
-             3.8           1.4472
-               4          1.42111
-&
- at TARGET S1
- at TYPE xy
-             0.2          1.47322
-             0.4          1.55476
-             0.6          1.59207
-             0.8          1.78017
-               1          1.84864
-             1.2          1.91801
-             1.4          1.98137
-             1.6          2.02379
-             1.8          2.04651
-               2          1.97898
-             2.2           1.8692
-             2.4          1.77966
-             2.6          1.71007
-             2.8          1.68304
-               3          1.66074
-             3.2          1.69572
-             3.4          1.74189
-             3.6          1.75861
-             3.8          1.73701
-               4          1.70112
-&
- at TARGET S2
- at TYPE xy
-             0.2         0.820432
-             0.4         0.928055
-             0.6          1.54623
-             0.8          2.02397
-               1          2.17887
-             1.2          2.32754
-             1.4          2.26773
-             1.6           2.2247
-             1.8          2.25371
-               2          2.18117
-             2.2          2.05487
-             2.4          1.88386
-             2.6          1.74661
-             2.8          1.78805
-               3          1.60581
-             3.2            1.529
-             3.4          1.47491
-             3.6          1.56524
-             3.8          1.92513
-               4          1.75687
-&
- at WITH G3
- at G3 ON
- at TARGET S0
- at TYPE xy
-             0.2          2.03295
-             0.4          2.05203
-             0.6          1.98895
-             0.8          2.14252
-               1          2.17004
-             1.2          2.20352
-             1.4          2.25053
-             1.6          2.29199
-             1.8          2.31257
-               2          2.28742
-             2.2          2.27729
-             2.4          2.23876
-             2.6          2.22835
-             2.8          2.22469
-               3          2.21548
-             3.2          2.24375
-             3.4          2.20799
-             3.6          2.17218
-             3.8          2.14461
-               4          2.11864
-&
- at TARGET S1
- at TYPE xy
-             0.2           1.9949
-             0.4          2.03728
-             0.6          2.03762
-             0.8          2.16521
-               1          2.21894
-             1.2          2.28223
-             1.4          2.34245
-             1.6          2.38286
-             1.8           2.4038
-               2          2.33395
-             2.2          2.22255
-             2.4          2.13228
-             2.6          2.06226
-             2.8          2.03513
-               3          2.01281
-             3.2          2.04821
-             3.4          2.09475
-             3.6          2.11153
-             3.8          2.08982
-               4          2.05384
-&
- at TARGET S2
- at TYPE xy
-             0.2          1.31703
-             0.4          1.42469
-             0.6          1.79595
-             0.8          2.02397
-               1          2.17887
-             1.2          2.32754
-             1.4          2.26773
-             1.6           2.2247
-             1.8          2.25371
-               2          2.18117
-             2.2          2.05487
-             2.4          1.88386
-             2.6          1.74661
-             2.8          1.78805
-               3          1.60581
-             3.2            1.529
-             3.4          1.47491
-             3.6          1.56524
-             3.8          1.92513
-               4          1.75687
-&
diff --git a/test/euler/scripts/merging.sh b/test/euler/scripts/merging.sh
deleted file mode 100755
index 5f40563..0000000
--- a/test/euler/scripts/merging.sh
+++ /dev/null
@@ -1,275 +0,0 @@
-#! /bin/sh
-
-usage()
-{
-    cat <<EOF
-Usage: merging.sh [OPTIONS]
-Options:
-	[--convective]
-EOF
-    exit $1
-}
-
-while test $# -gt 0; do
-  case "$1" in
-  -*=*) optarg=`echo "$1" | sed 's/[-_a-zA-Z0-9]*=//'` ;;
-  *) optarg= ;;
-  esac
-
-  case $1 in
-    --convective)
-      convective="AdvectionParams {
-    flux = gfs_face_velocity_convective_flux
-  }"
-      ;;
-    --*)
-      usage 1 1>&2
-      ;;
-  esac
-  shift
-done
-
-if test -e merging; then 
-    rm -r -f merging
-fi
-mkdir merging
-mkdir merging/run1
-mkdir merging/run2
-mkdir merging/run3
-
-tmax=4.0
-cd merging/run1
-cat <<EOF > merging.gfs
-1 0 GfsSimulation GfsBox GfsGEdge {} {
-  Time { end = $tmax }
-  $convective
-  Refine {
-    double r = sqrt (x*x + y*y); 
-    return r < 0.03125 ? 10 : r < 0.0625 ? 9 : r < 0.125 ? 8 : r < 0.25 ? 7 : 6;
-  }
-  InitVorticity {} {
-    double gaussian (double xo, double yo, double scale) {
-      return 2.*M_PI*exp (- 2.*((x - xo)*(x - xo) + (y - yo)*(y - yo))/(scale*scale));
-    }
-    return gaussian (0, 0.01, 0.01) + gaussian (0, -0.01, 0.01);
-  }
-  OutputTime { istep = 1 } stdout
-  OutputScalarNorm { istep = 1 } stdout { v = Divergence }
-  OutputProjectionStats { istep = 1 } stdout
-  OutputSimulation { step = 0.2 } sim-%3.1f {}
-  OutputTiming { start = end } stdout
-}
-GfsBox {}
-EOF
-gerris2D merging.gfs > log
-
-cd ../run2
-cat <<EOF > merging.gfs
-1 0 GfsSimulation GfsBox GfsGEdge {} {
-  Time { end = $tmax }
-  $convective
-  Refine {
-    double r = sqrt (x*x + y*y); 
-    return r < 0.03125 ? 11 : r < 0.0625 ? 10 : r < 0.09375 ? 9 : r < 0.125 ? 8 : r < 0.25 ? 7 : 6;
-  }
-  InitVorticity {} {
-    double gaussian (double xo, double yo, double scale) {
-      return 2.*M_PI*exp (- 2.*((x - xo)*(x - xo) + (y - yo)*(y - yo))/(scale*scale));
-    }
-    return gaussian (0, 0.01, 0.01) + gaussian (0, -0.01, 0.01);
-  }
-  OutputTime { istep = 1 } stdout
-  OutputScalarNorm { istep = 1 } stdout { v = Divergence }
-  OutputProjectionStats { istep = 1 } stdout
-  OutputSimulation { step = 0.2 } sim-%3.1f {}
-  OutputTiming { start = end } stdout
-}
-GfsBox {}
-EOF
-gerris2D merging.gfs > log
-
-cd ../run3
-cat <<EOF > merging.gfs
-1 0 GfsSimulation GfsBox GfsGEdge {} {
-  Time { end = $tmax }
-  $convective
-  Refine {
-    double r = sqrt (x*x + y*y); 
-    return r < 0.03125 ? 12 : r < 0.046875 ? 11 : r < 0.0625 ? 10 : r < 0.09375 ? 9 : r < 0.125 ? 8 : r < 0.25 ? 7 : 6;
-  }
-  InitVorticity {} {
-    double gaussian (double xo, double yo, double scale) {
-      return 2.*M_PI*exp (- 2.*((x - xo)*(x - xo) + (y - yo)*(y - yo))/(scale*scale));
-    }
-    return gaussian (0, 0.01, 0.01) + gaussian (0, -0.01, 0.01);
-  }
-  OutputTime { istep = 1 } stdout
-  OutputScalarNorm { istep = 1 } stdout { v = Divergence }
-  OutputProjectionStats { istep = 1 } stdout
-  OutputSimulation { step = 0.2 } sim-%3.1f {}
-  OutputTiming { start = end } stdout
-}
-GfsBox {}
-EOF
-gerris2D merging.gfs > log
-cd ..
-
-uerror=`mktemp /tmp/uerror.XXXXXX`
-for time in `seq 0.2 0.2 $tmax`; do
-    formatted=`echo $time | awk '{printf ("%3.1f", $1);}'`
-    run1=`gfscompare2D -r -n -v run1/sim-$formatted run2/sim-$formatted U 2>&1 | awk '{ if ($2 == "err") printf ("%g %g %g ", $4, $6, $8);}'`
-    run1="$run1 `gfscompare2D -r -n -v run2/sim-$formatted run3/sim-$formatted U 2>&1 | awk '{ if ($2 == "err") printf (\"%g %g %g \", $4, $6, $8); }'`"
-    echo $time $run1 >> $uerror
-done
-
-echo "@description \"merging.sh\""
-
-echo "@WITH G0"
-echo "@G0 ON"
-echo "@G0 TYPE logy"
-echo "@XAXIS LABEL \"Time\""
-echo "@xaxis label char size 0.6"
-echo "@xaxis ticklabel char size 0.6"
-echo "@YAXIS LABEL \"Total error\""
-echo "@yaxis label char size 0.6"
-echo "@yaxis ticklabel char size 0.6"
-
-echo "@LEGEND STRING 0 \"L1 norm (run1)\""
-echo "@TARGET S0"
-echo "@TYPE xy" 
-awk '{print $1 " " $2}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 1 \"L2 norm (run1)\""
-echo "@TARGET S1"
-echo "@TYPE xy" 
-awk '{print $1 " " $3}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 2 \"Lmax norm (run1)\""
-echo "@TARGET S2"
-echo "@TYPE xy" 
-awk '{print $1 " " $4}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 3 \"L1 norm (run2)\""
-echo "@TARGET S3"
-echo "@TYPE xy" 
-awk '{print $1 " " $8}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 4 \"L2 norm (run2)\""
-echo "@TARGET S4"
-echo "@TYPE xy" 
-awk '{print $1 " " $9}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 5 \"Lmax norm (run2)\""
-echo "@TARGET S5"
-echo "@TYPE xy" 
-awk '{print $1 " " $10}' < $uerror
-echo "&"
-
-echo "@WITH G1"
-echo "@G1 ON"
-echo "@G1 TYPE logy"
-echo "@XAXIS LABEL \"Time\""
-echo "@xaxis label char size 0.6"
-echo "@xaxis ticklabel char size 0.6"
-echo "@YAXIS LABEL \"Refined error\""
-echo "@yaxis label char size 0.6"
-echo "@yaxis ticklabel char size 0.6"
-
-echo "@LEGEND STRING 0 \"L1 norm (run1)\""
-echo "@TARGET S0"
-echo "@TYPE xy" 
-awk '{print $1 " " $5}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 1 \"L2 norm (run1)\""
-echo "@TARGET S1"
-echo "@TYPE xy" 
-awk '{print $1 " " $6}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 2 \"Lmax norm (run1)\""
-echo "@TARGET S2"
-echo "@TYPE xy" 
-awk '{print $1 " " $7}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 3 \"L1 norm (run2)\""
-echo "@TARGET S3"
-echo "@TYPE xy" 
-awk '{print $1 " " $11}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 4 \"L2 norm (run2)\""
-echo "@TARGET S4"
-echo "@TYPE xy" 
-awk '{print $1 " " $12}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 5 \"Lmax norm (run2)\""
-echo "@TARGET S5"
-echo "@TYPE xy" 
-awk '{print $1 " " $13}' < $uerror
-echo "&"
-
-echo "@WITH G2"
-echo "@G2 ON"
-echo "@G2 TYPE xy"
-echo "@XAXIS LABEL \"Time\""
-echo "@xaxis label char size 0.6"
-echo "@xaxis ticklabel char size 0.6"
-echo "@YAXIS LABEL \"Total order\""
-echo "@yaxis label char size 0.6"
-echo "@yaxis ticklabel char size 0.6"
-
-echo "@LEGEND STRING 0 \"L1 norm\""
-echo "@TARGET S0"
-echo "@TYPE xy" 
-awk '{print $1 " " log($2/$8)/log(2)}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 1 \"L2 norm\""
-echo "@TARGET S1"
-echo "@TYPE xy" 
-awk '{print $1 " " log($3/$9)/log(2)}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 2 \"Lmax norm\""
-echo "@TARGET S2"
-echo "@TYPE xy" 
-awk '{print $1 " " log($4/$10)/log(2)}' < $uerror
-echo "&"
-
-echo "@WITH G3"
-echo "@G3 ON"
-echo "@G3 TYPE xy"
-echo "@XAXIS LABEL \"Time\""
-echo "@xaxis label char size 0.6"
-echo "@xaxis ticklabel char size 0.6"
-echo "@YAXIS LABEL \"Refined order\""
-echo "@yaxis label char size 0.6"
-echo "@yaxis ticklabel char size 0.6"
-
-echo "@LEGEND STRING 0 \"L1 norm\""
-echo "@TARGET S0"
-echo "@TYPE xy" 
-awk '{print $1 " " log($5/$11)/log(2)}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 1 \"L2 norm\""
-echo "@TARGET S1"
-echo "@TYPE xy" 
-awk '{print $1 " " log($6/$12)/log(2)}' < $uerror
-echo "&"
-
-echo "@LEGEND STRING 2 \"Lmax norm\""
-echo "@TARGET S2"
-echo "@TYPE xy" 
-awk '{print $1 " " log($7/$13)/log(2)}' < $uerror
-echo "&"
-
-rm -f $uerror
diff --git a/test/euler/template.tex b/test/euler/template.tex
index 8e1aa5c..6238165 100644
--- a/test/euler/template.tex
+++ b/test/euler/template.tex
@@ -25,6 +25,7 @@
 \input{reynolds/reynolds.tex}
 \input{reynolds/box/box.tex}
 \input{periodic/periodic.tex}
+\input{merging/merging.tex}
 
 \bibliographystyle{plain}
 \bibliography{tests}

-- 
Gerris Flow Solver



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