[SCM] Gerris Flow Solver branch, upstream, updated. b3aa46814a06c9cb2912790b23916ffb44f1f203
Stephane Popinet
popinet at users.sf.net
Fri May 15 02:54:53 UTC 2009
The following commit has been merged in the upstream branch:
commit 0836322934ab5fed519da291dc0e356a6a67eb37
Author: Stephane Popinet <popinet at users.sf.net>
Date: Wed Dec 19 15:44:14 2007 +1100
New Cook Strait tides example
darcs-hash:20071219044414-d4795-ec8cfe2a6660c148e89ccf7d01957a04a7317f38.gz
diff --git a/doc/examples/Makefile.am b/doc/examples/Makefile.am
index 5593758..8c4abda 100644
--- a/doc/examples/Makefile.am
+++ b/doc/examples/Makefile.am
@@ -5,7 +5,8 @@ EXAMPLES = \
rt \
boussinesq \
tangaroa \
- logo
+ logo \
+ tides
EXTRA_DIST = \
template.tex \
diff --git a/doc/examples/template.tex b/doc/examples/template.tex
index 6f7037b..d5e7642 100644
--- a/doc/examples/template.tex
+++ b/doc/examples/template.tex
@@ -55,6 +55,10 @@ The usefulness and quality of this document very much depend on the contribution
\input{tangaroa/tangaroa.tex}
+\section{Shallow-water}
+
+\input{tides/tides.tex}
+
\section{\label{howto}How to write examples}
This document is generated automatically using self-documenting Gerris parameter files. If you look at \htmladdnormallinkfoot{any}{cylinder/cylinder.gfs} of the {\tt .gfs} files in this document you will see that apart from comments on specific instructions, the top of the file contains fields which describe the simulation. They are:
diff --git a/test/geo/geo.gfv b/doc/examples/tides/amplitude.gfv
similarity index 79%
copy from test/geo/geo.gfv
copy to doc/examples/tides/amplitude.gfv
index d61f0af..70ec56f 100644
--- a/test/geo/geo.gfv
+++ b/doc/examples/tides/amplitude.gfv
@@ -1,8 +1,9 @@
# GfsView 3D
View {
tx = 0 ty = 0
+ sx = 1 sy = 1 sz = 1
q0 = 0 q1 = 0 q2 = 0 q3 = 1
- fov = 30
+ fov = 15.1725
r = 0.3 g = 0.4 b = 0.6
res = 1
lc = 0.001
@@ -15,7 +16,7 @@ Squares {
} {
n.x = 0 n.y = 0 n.z = 1
pos = -0.5
-} E {
+} sqrt(A0*A0+B0*B0)*5000./19.62 {
amin = 1
amax = 1
cmap = Jet
diff --git a/doc/examples/tides/bathymetry b/doc/examples/tides/bathymetry
new file mode 100644
index 0000000..8b0ccbb
--- /dev/null
+++ b/doc/examples/tides/bathymetry
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diff --git a/doc/examples/tides/coefficients b/doc/examples/tides/coefficients
new file mode 100644
index 0000000..e20674b
--- /dev/null
+++ b/doc/examples/tides/coefficients
@@ -0,0 +1,6412 @@
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+174.901 -40.7937 0.610847 -60.400314
+174.729 -40.9236 0.492866 -69.432388
+174.774 -40.9338 0.485370 -67.262543
+174.825 -41.038 0.412826 -64.677658
+174.838 -41.0244 0.425988 -64.065941
+174.744 -40.958 0.463539 -69.336899
+174.767 -40.8993 0.513153 -67.051529
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+174.821 -40.9731 0.459686 -65.184380
+174.807 -40.881 0.528812 -64.849968
+174.834 -40.8946 0.518189 -63.815208
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+174.649 -41.022 0.405040 -77.705177
+174.451 -41.0344 0.453746 -92.361977
+174.489 -41.0691 0.397385 -94.715744
+174.427 -41.1243 0.370830 -111.261147
+174.47 -41.113 0.357709 -103.789169
+174.505 -41.029 0.431858 -88.780647
+174.552 -41.0541 0.388233 -87.812317
+174.789 -41.0138 0.421720 -67.218147
+174.816 -41.0234 0.420510 -65.464478
+174.602 -41.0296 0.402363 -81.771019
+174.636 -41.0547 0.372139 -80.504776
+174.626 -41.1272 0.297130 -85.490814
+174.666 -41.1078 0.319684 -79.667259
+174.646 -40.9493 0.475124 -74.725311
+174.697 -40.9527 0.468524 -71.872879
+174.525 -41.2574 0.184114 -143.160599
+174.556 -41.2871 0.160574 -165.372665
+174.547 -41.3378 0.246810 171.969376
+174.59 -41.3138 0.181604 170.100952
+174.686 -41.3707 0.377671 146.540085
+174.68 -41.4073 0.406002 149.175400
+174.608 -41.3447 0.248003 157.078369
+174.638 -41.3766 0.340945 151.133102
+174.195 -40.4423 0.907411 -68.582596
+174.26 -40.4289 0.890212 -67.871468
+174.67 -40.9876 0.438046 -74.630623
+174.719 -40.9879 0.437100 -71.445259
+174.584 -41.0935 0.337434 -88.325546
+174.601 -41.0638 0.366669 -84.305885
+174.538 -41.3927 0.338483 164.715195
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+174.878 -41.4708 0.525992 145.516556
+174.63 -41.0873 0.339431 -82.834366
+174.668 -41.0762 0.350400 -78.463028
+174.785 -40.9637 0.461554 -67.104263
+174.796 -40.9879 0.442792 -66.794952
+174.928 -40.7059 0.663510 -60.472012
+174.981 -40.6916 0.676280 -59.416199
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+174.155 -40.8353 0.752773 -82.838165
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+174.996 -41.515 0.551651 145.567856
+174.863 -41.5029 0.529009 146.473953
+174.88 -41.5463 0.542893 146.938385
+174.658 -41.1613 0.263156 -81.930557
+174.67 -41.1349 0.293135 -79.786064
+174.068 -41.4155 0.512642 179.833466
+174.106 -41.4222 0.506090 179.632050
+174.071 -41.4482 0.516095 178.793152
+174.069 -41.4788 0.521585 177.857437
+174.188 -41.5664 0.555144 170.101608
+174.23 -41.5846 0.558861 167.531464
+174.358 -41.668 0.576150 158.584366
+174.375 -41.7096 0.592406 155.883820
+174.328 -41.8112 0.629787 151.102600
+174.374 -41.8413 0.624002 150.010712
+174.209 -41.6877 0.611316 161.581360
+174.253 -41.7059 0.612233 159.633667
+174.67 -41.5282 0.486680 151.941635
+174.732 -41.5103 0.492965 149.572647
+174.745 -41.9146 0.607115 146.896255
+174.781 -41.8452 0.600202 147.397903
+175.027 -41.4108 0.544826 144.626755
+175.076 -41.4195 0.548473 144.490982
+174.776 -41.0429 0.396539 -67.703018
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+174.817 -41.0694 0.389887 -64.545692
+174.799 -41.0592 0.392035 -65.734940
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+174.843 -41.0404 0.417341 -63.563881
diff --git a/doc/examples/tides/ellipses.gfv b/doc/examples/tides/ellipses.gfv
new file mode 100644
index 0000000..c900183
--- /dev/null
+++ b/doc/examples/tides/ellipses.gfv
@@ -0,0 +1,26 @@
+# GfsView 3D
+View {
+ tx = -0.11839 ty = 0.0263953
+ sx = 1 sy = 1 sz = 1
+ q0 = 0 q1 = 0 q2 = 0 q3 = 1
+ fov = 2.66573
+ r = 1 g = 1 b = 1
+ res = 1
+ lc = 0.001
+ reactivity = 0.1
+}
+Ellipses {
+ r = 0 g = 0 b = 0
+ shading = Constant
+ maxlevel = -1
+} {
+ n.x = 0 n.y = 0 n.z = 1
+ pos = -0.5
+} sqrt(AU0*AU0+AV0*AV0+BU0*BU0+BV0*BV0)*500e3*1e-4 {
+ amin = 0 min = 0
+ amax = 0 max = 2
+ cmap = Jet
+} AU0 AV0 BU0 BV0 {
+ scale = 0.1715
+ use_scalar = 1
+}
diff --git a/test/geo/geo.gfv b/doc/examples/tides/phase.gfv
similarity index 81%
copy from test/geo/geo.gfv
copy to doc/examples/tides/phase.gfv
index d61f0af..ad6f5a9 100644
--- a/test/geo/geo.gfv
+++ b/doc/examples/tides/phase.gfv
@@ -1,8 +1,9 @@
# GfsView 3D
View {
tx = 0 ty = 0
+ sx = 1 sy = 1 sz = 1
q0 = 0 q1 = 0 q2 = 0 q3 = 1
- fov = 30
+ fov = 15.5877
r = 0.3 g = 0.4 b = 0.6
res = 1
lc = 0.001
@@ -15,7 +16,7 @@ Squares {
} {
n.x = 0 n.y = 0 n.z = 1
pos = -0.5
-} E {
+} atan2(B0,A0)*180./M_PI {
amin = 1
amax = 1
cmap = Jet
diff --git a/test/geo/geo.gfv b/doc/examples/tides/residual.gfv
similarity index 53%
copy from test/geo/geo.gfv
copy to doc/examples/tides/residual.gfv
index d61f0af..a6d48f9 100644
--- a/test/geo/geo.gfv
+++ b/doc/examples/tides/residual.gfv
@@ -1,22 +1,26 @@
# GfsView 3D
View {
- tx = 0 ty = 0
+ tx = -0.11839 ty = 0.0263953
+ sx = 1 sy = 1 sz = 1
q0 = 0 q1 = 0 q2 = 0 q3 = 1
- fov = 30
- r = 0.3 g = 0.4 b = 0.6
+ fov = 2.66573
+ r = 1 g = 1 b = 1
res = 1
lc = 0.001
reactivity = 0.1
}
-Squares {
+Vectors {
r = 0 g = 0 b = 0
shading = Constant
maxlevel = -1
} {
n.x = 0 n.y = 0 n.z = 1
pos = -0.5
-} E {
+} sqrt(ZU*ZU+ZV*ZV)*500e3*1e-4 {
amin = 1
- amax = 1
+ amax = 0 max = 0.6
cmap = Jet
+} ZU ZV 0 {
+ scale = 1
+ use_scalar = 1
}
diff --git a/doc/examples/tides/tides.gfs b/doc/examples/tides/tides.gfs
new file mode 100644
index 0000000..c31a736
--- /dev/null
+++ b/doc/examples/tides/tides.gfs
@@ -0,0 +1,203 @@
+# Title: Lunar tides in Cook Strait, New Zealand
+#
+# Description:
+#
+# The shallow-water equations are solved using the "ocean" version of
+# Gerris. The tidal elevations for the lunar (M2) component obtained
+# from a larger-area tidal model are imposed as conditions on
+# the boundaries of the domain.
+#
+# The comments in the \htmladdnormallinkfoot{tides.sh}{tides/tides.sh}
+# script describe how to generate the appropriate GTS files from the
+# tidal elevation and bathymetry data.
+#
+# After an initial transient ($t < \approx 1$ day) due to relaxation of
+# the model toward a state consistent with the mathematical model and
+# with the imposed boundary conditions, the model reaches a periodic
+# regime (Figure \ref{periodic}).
+#
+# \begin{figure}[htbp]
+# \caption{\label{periodic}Evolution of the maximum velocity and
+# elevation with time.}
+# \begin{center}
+# \includegraphics[width=0.8\hsize]{pv.eps}
+# \end{center}
+# \end{figure}
+#
+# Online harmonic decomposition can then be used to extract the
+# amplitudes and phases of the computed M2 tidal components. The
+# simulation stops automatically when convergence of the harmonic
+# decomposition is reached (Figure \ref{harmcon}).
+#
+# \begin{figure}[htbp]
+# \caption{\label{harmcon}Convergence of the maximum tidal amplitude
+# (estimated from harmonic decomposition) with time.}
+# \begin{center}
+# \includegraphics[width=0.8\hsize]{a0.eps}
+# \end{center}
+# \end{figure}
+#
+# The final tidal amplitudes and phases are illustrated in Figures
+# \ref{amplitude} and \ref{phase} respectively. The harmonic
+# decomposition is also applied to the velocity field. The results can
+# be represented as tidal ellipses (Figure \ref{ellipses}) and
+# residual currents (Figure \ref{residual}).
+#
+# Note that the results for this simulation will not be as good as
+# these described in Rym Msadek's \htmladdnormallinkfoot{technical
+# report}{http://gfs.sf.net/tides.pdf} because iterative Flather
+# conditions have not been applied. See the report for details.
+#
+# \begin{figure}[htbp]
+# \caption{\label{amplitude}Tidal amplitude estimated from the harmonic
+# decomposition. Dark red is 1.4 metres, dark blue is 0.}
+# \begin{center}
+# \includegraphics[width=0.8\hsize]{amplitude.eps}
+# \end{center}
+# \end{figure}
+#
+# \begin{figure}[htbp]
+# \caption{\label{phase}Tidal phase estimated from the harmonic
+# decomposition. Dark red is 180 degrees, dark blue -180 degrees.}
+# \begin{center}
+# \includegraphics[width=0.8\hsize]{phase.eps}
+# \end{center}
+# \end{figure}
+#
+# \begin{figure}[htbp]
+# \caption{\label{ellipses}Detail of tidal ellipses estimated from the harmonic
+# decomposition coloured according to maximum current speed. Dark red
+# is 2 metres/sec, dark blue is zero.}
+# \begin{center}
+# \includegraphics[width=0.8\hsize]{ellipses.eps}
+# \end{center}
+# \end{figure}
+#
+# \begin{figure}[htbp]
+# \caption{\label{residual}Detail of residual tidal currents estimated from the
+# harmonic decomposition coloured according to residual current speed.
+# Dark red is 0.6 metres/sec, dark blue is zero.}
+# \begin{center}
+# \includegraphics[width=0.8\hsize]{residual.eps}
+# \end{center}
+# \end{figure}
+#
+# Author: St\'ephane Popinet
+# Command: sh tides.sh
+# Version: 1.1.2
+# Required files: tides.sh bathymetry coefficients amplitude.gfv ellipses.gfv phase.gfv residual.gfv tides.gfv
+# Running time: 2 hours
+# Generated files: a0.eps amplitude.eps ellipses.eps phase.eps pv.eps residual.eps
+
+# Reference depth (metres)
+Define H0 5000.
+
+# Box size (metres)
+Define L0 500e3
+
+# Coriolis parameter (s^-1)
+Define F0 1e-4
+
+# M2 tidal frequency. The period is 12h25 (44700 seconds).
+Define M2F (2.*M_PI/(44700.*F0))
+
+# M2 tidal elevation
+Define M2(t) (A_amp*cos (M2F*t)+B_amp*sin (M2F*t))
+
+# Use the "GfsOcean" model
+1 0 GfsOcean GfsBox GfsGEdge {} {
+ # Set the timestep to sthg small compared to the tidal period
+ Time { dtmax = 1e-2 }
+
+ # Refine to six levels
+ Refine 6
+
+ # We want more accuracy in the projection than the default 1e-3
+ ApproxProjectionParams { tolerance = 1e-6 nitermax = 10 }
+
+ # Initialise tidal amplitudes
+ Init {} {
+ A_amp = AM2.gts
+ B_amp = BM2.gts
+ }
+
+ # Bathymetry
+ Solid bath.gts
+
+ # Refine the coastline to 10 levels
+ RefineSurface 10 bath.gts { twod = 1 }
+
+ # Non-dimensional gravity
+ PhysicalParams { g = 19.62 }
+
+ # Add Coriolis source term
+ SourceCoriolis -1.
+
+ # Bottom friction parameterisation
+ Init { istep = 1 } {
+ U = U/(1. + dt*fabs(U)*0.04*S/A)
+ V = V/(1. + dt*fabs(V)*0.04*S/A)
+ }
+
+ # Weak exponential filtering of the velocity field
+ # EventFilter { istep = 1 } U 4
+ # EventFilter { istep = 1 } V 4
+
+ # After t=10, starts on-the-fly harmonic decomposition of the pressure field...
+ EventHarmonic { start = 10 istep = 10 } P A B Z EP M2F
+ # ... and of the velocity field
+ EventHarmonic { start = 10 istep = 10 } U AU BU ZU EU M2F
+ EventHarmonic { start = 10 istep = 10 } V AV BV ZV EV M2F
+
+ # After t=10, stops the simulation if the variations of the A0
+ # harmonic component are less than 1e-5 in 100 timesteps
+ EventStop { start = 10 istep = 100 } A0 1e-5
+
+ OutputTime { istep = 1 } stderr
+ OutputProjectionStats { istep = 1 } stderr
+
+ # Output solution on standard output every 20 timesteps
+ # for on-the-fly visualisation with GfsView
+ # Do not include the GTS file for the embedded surface to save bandwidth
+ OutputSimulation { istep = 20 } stdout { solid = 0 }
+
+ # Output solution in file 'end.gfs' at the end of the simulation
+ OutputSimulation { start = end } end.gfs
+
+ # Output curves using gnuplot
+ EventScript { start = end } {
+ cat <<EOF | gnuplot
+ set term postscript eps lw 3 solid 20 colour
+ set output 'pv.eps'
+ set xlabel 'Time (days)'
+ set ylabel 'Elevation (metres) or Velocity (metres/s)'
+ plot 'p' u (\$3/(F0*86400.)):(\$9*H0/19.62) w l t "Elevation", \
+ 'u' u (\$3/(F0*86400.)):(\$9*L0*F0) w l t "Velocity"
+ set output 'a0.eps'
+ set ylabel 'Maximum harmonic elevation (metres)'
+ plot [1:]'a0' u (\$3/(F0*86400.)):(\$9*H0/19.62) w l t ""
+EOF
+ }
+
+ OutputScalarNorm { istep = 1 } p { v = P }
+ OutputScalarNorm { istep = 1 } u { v = Velocity }
+ OutputScalarNorm { istep = 1 } a0 { v = sqrt(A0*A0 + B0*B0) }
+}
+GfsBox {
+ # Use Flather boundary conditions on all boundaries
+ left = Boundary {
+ BcFlather U 0 H P M2(t)
+ }
+ right = Boundary {
+ BcFlather U 0 H P M2(t)
+ }
+ top = Boundary {
+ BcFlather V 0 H P M2(t)
+ }
+ bottom = Boundary {
+ BcFlather V 0 H P M2(t)
+ }
+
+ # This is required for consistent free-surface fluxes
+ front = Boundary
+}
diff --git a/test/geo/geo.gfv b/doc/examples/tides/tides.gfv
similarity index 76%
copy from test/geo/geo.gfv
copy to doc/examples/tides/tides.gfv
index d61f0af..c886916 100644
--- a/test/geo/geo.gfv
+++ b/doc/examples/tides/tides.gfv
@@ -1,22 +1,25 @@
# GfsView 3D
View {
tx = 0 ty = 0
+ sx = 1 sy = 1 sz = 1
q0 = 0 q1 = 0 q2 = 0 q3 = 1
- fov = 30
+ fov = 15.1811
r = 0.3 g = 0.4 b = 0.6
res = 1
lc = 0.001
reactivity = 0.1
}
-Squares {
+Linear {
r = 0 g = 0 b = 0
shading = Constant
maxlevel = -1
} {
n.x = 0 n.y = 0 n.z = 1
pos = -0.5
-} E {
+} P*5000./19.62 {
amin = 1
amax = 1
cmap = Jet
+} {
+ scale = 0
}
diff --git a/doc/examples/tides/tides.sh b/doc/examples/tides/tides.sh
new file mode 100644
index 0000000..c7a7167
--- /dev/null
+++ b/doc/examples/tides/tides.sh
@@ -0,0 +1,91 @@
+# GMT path
+PATH=$PATH:/usr/lib/gmt/bin
+
+# The Gerris ocean model uses the following non-dimensional variables
+#
+# Dimensional variables:
+# gravity:
+# g* = 9.81 m/s^2
+# reference depth:
+# H* = 5000 m
+# reference length:
+# L* = 500 km
+# Coriolis f-plane:
+# f* = 1e-4 s^-1
+# Velocity:
+# u* = ... m/s
+# Time:
+# t* = ... s
+# Surface elevation:
+# eta* = ... m
+# Position:
+# x* = ... m
+#
+# Corresponding non-dimensional variables
+# g = g*H*/L*^2f*^2 = 19.62
+# u = u*/L*f*
+# t = t*f*
+# x = x*/L*
+# eta = eta*/H*
+# pressure:
+# p = eta g
+#
+# -- create bathymetry --
+# The domain is centered on lon,lat (deg): 174,-40.8
+# default domain size is 500 km
+# --angle=40 means that the resulting projection will also be rotated by 40 degrees
+# --rel is the relative error allowed when simplifying bathymetry i.e. 2.5% of the total depth
+# bathymetry: contains three columns lon (deg), lat (deg), depth (m)
+#
+# bat2gts also creates two scripts: xy2lolat and lolat2xy which
+# convert coordinates in input between a lon,lat coordinates system
+# to/from the x,y, coordinate system in which Gerris works.
+bat2gts --lat=-40.8 --long=174 --angle=40 --rel=0.025 < bathymetry | transform --tz -0.4994 > bath.gts
+
+# M2 tidal coefficients
+#
+# coefficients contains the amplitude and phase of the M2
+# tide as a function of space i.e. four columns:
+# lon (deg) lat (deg) amplitude (m) phase (degree)
+
+# just counts the number of lines in the input file
+lines=`wc -l coefficients | awk '{print $1}'`
+
+# transform lon,lat into x,y coordinates
+# Gerris defines the tidal M2 mode as:
+# AM2*cos (omega*t) + BM2*sin (omega*t)
+#
+# We first compute A_amp from the amplitude and phase.
+# We also need to rescale the tidal amplitude according to:
+# eta = eta*g/H*
+./lolat2xy < coefficients | awk -v lines=$lines '
+BEGIN {
+ print lines " 0 0"
+} {
+ H = 5000
+ g = 19.62
+ amp = $3
+ phi = $4*3.14159265357/180.
+ print $1 " " $2 " " g*amp/H*cos(phi)
+}' | delaunay > AM2.gts
+
+# Now compute BM2
+./lolat2xy < coefficients | awk -v lines=$lines '
+BEGIN {
+ print lines " 0 0"
+} {
+ H = 5000
+ g = 19.62
+ amp = $3
+ phi = $4*3.14159265357/180.
+ print $1 " " $2 " " g*amp/H*sin(phi)
+}' | delaunay > BM2.gts
+
+# Run the simulation
+gerris2D3 -m tides.gfs | gfsview2D3 tides.gfv
+
+# Use batch mode of gfsview to generate figures
+echo "Save amplitude.eps { format = EPS }" | gfsview-batch2D3 end.gfs amplitude.gfv
+echo "Save phase.eps { format = EPS }" | gfsview-batch2D3 end.gfs phase.gfv
+echo "Save ellipses.eps { format = EPS }" | gfsview-batch2D3 end.gfs ellipses.gfv
+echo "Save residual.eps { format = EPS }" | gfsview-batch2D3 end.gfs residual.gfv
--
Gerris Flow Solver
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