[SCM] Gerris Flow Solver branch, upstream, updated. b3aa46814a06c9cb2912790b23916ffb44f1f203
Stephane Popinet
popinet at users.sf.net
Fri May 15 02:55:41 UTC 2009
The following commit has been merged in the upstream branch:
commit 71b480cbc0cfcf659b43d9b7bb72b17cac691ae0
Author: Stephane Popinet <popinet at users.sf.net>
Date: Sat Sep 6 07:30:55 2008 +1000
Axisymmetric viscous flow past a sphere test case
darcs-hash:20080905213055-d4795-7d9df7743ff11eee3c3c46b2d151c49b8faf3241.gz
diff --git a/test/axi/viscous/Re-12 b/test/axi/viscous/Re-12
new file mode 100644
index 0000000..4094da1
--- /dev/null
+++ b/test/axi/viscous/Re-12
@@ -0,0 +1,12 @@
+20 100 0.00601338 0.00214903
+30 100 0.144321 -1.54293e-05
+40 100 0.281624 0.000964816
+50 100 0.405324 2.30829e-05
+60 100 0.51502 2.97476e-05
+80 22.7 0.703601 0.000283994
+100 28.1 0.86826 -0.00022001
+120 31.4 1.01188 -1.2337e-05
+150 31.5 1.19646 -6.03988e-05
+200 36.2 1.44074 -6.93522e-05
+250 76 1.62679 -2.93692e-06
+300 100 1.76844 -1.06835e-07
diff --git a/test/axi/viscous/blanco-1995 b/test/axi/viscous/blanco-1995
new file mode 100644
index 0000000..d341ff4
--- /dev/null
+++ b/test/axi/viscous/blanco-1995
@@ -0,0 +1,4 @@
+20.0453 0
+38.4509 0.46092
+70.6662 1.22222
+99.8764 1.72006
diff --git a/test/axi/viscous/cp-12-200 b/test/axi/viscous/cp-12-200
new file mode 100644
index 0000000..e173896
--- /dev/null
+++ b/test/axi/viscous/cp-12-200
@@ -0,0 +1,162 @@
+0.0122082 1.03596
+0.036632 1.03337
+0.0610778 1.02801
+0.08556 1.01973
+0.110094 1.00848
+0.134694 0.994156
+0.159377 0.97694
+0.184158 0.963758
+0.206752 0.95857
+0.219232 0.956152
+0.234084 0.941808
+0.259263 0.90893
+0.284612 0.879878
+0.303968 0.867636
+0.316787 0.86038
+0.335899 0.834982
+0.361881 0.79477
+0.378716 0.777
+0.391904 0.765906
+0.414648 0.733718
+0.435666 0.70047
+0.449168 0.686672
+0.468673 0.657964
+0.489793 0.621894
+0.503675 0.60358
+0.52422 0.569548
+0.542272 0.533592
+0.556615 0.51391
+0.579278 0.479456
+0.593887 0.455112
+0.611131 0.426434
+0.630019 0.387948
+0.645253 0.36276
+0.665318 0.328058
+0.680918 0.298664
+0.700022 0.264834
+0.716033 0.235808
+0.734326 0.203932
+0.7508 0.174536
+0.768399 0.143297
+0.785398 0.113224
+0.802397 0.0835276
+0.819997 0.0534478
+0.83647 0.0237254
+0.854763 -0.00820992
+0.870775 -0.0372544
+0.889878 -0.0703106
+0.905479 -0.0983104
+0.925544 -0.129695
+0.940778 -0.150842
+0.959665 -0.183019
+0.976909 -0.207078
+0.991519 -0.230668
+1.01418 -0.26238
+1.02852 -0.278202
+1.04658 -0.308696
+1.06712 -0.337024
+1.081 -0.351164
+1.10212 -0.378892
+1.12163 -0.399754
+1.13513 -0.40825
+1.15615 -0.4347
+1.17889 -0.458974
+1.19208 -0.46304
+1.20891 -0.470916
+1.2349 -0.50155
+1.25401 -0.519646
+1.26683 -0.51963
+1.28618 -0.519728
+1.31153 -0.537734
+1.33671 -0.561508
+1.35156 -0.56906
+1.36404 -0.564762
+1.38664 -0.555342
+1.41142 -0.554992
+1.4361 -0.561374
+1.4607 -0.564578
+1.48524 -0.565088
+1.50972 -0.563096
+1.53416 -0.558486
+1.55859 -0.551548
+1.583 -0.542996
+1.60743 -0.533548
+1.63187 -0.523638
+1.65636 -0.513396
+1.68089 -0.502784
+1.70549 -0.49173
+1.73017 -0.480044
+1.75495 -0.46499
+1.77755 -0.450128
+1.79003 -0.443966
+1.80488 -0.437696
+1.83006 -0.427432
+1.85541 -0.414374
+1.87476 -0.40278
+1.88758 -0.396722
+1.90669 -0.388444
+1.93268 -0.376222
+1.94951 -0.367008
+1.9627 -0.36128
+1.98544 -0.351782
+2.00646 -0.342482
+2.01996 -0.337486
+2.03947 -0.329846
+2.06059 -0.320994
+2.07447 -0.316432
+2.09502 -0.309344
+2.11307 -0.302192
+2.12741 -0.297794
+2.15007 -0.291136
+2.16468 -0.287044
+2.18193 -0.28244
+2.20081 -0.276632
+2.21605 -0.272968
+2.23611 -0.268362
+2.25171 -0.264858
+2.27082 -0.260936
+2.28683 -0.25778
+2.30512 -0.254544
+2.3216 -0.251754
+2.3392 -0.249158
+2.35619 -0.246772
+2.37319 -0.2446
+2.39079 -0.242494
+2.40727 -0.24068
+2.42556 -0.238842
+2.44157 -0.23724
+2.46067 -0.235464
+2.47627 -0.233902
+2.49634 -0.232184
+2.51157 -0.231044
+2.53046 -0.229146
+2.54771 -0.22774
+2.56232 -0.226114
+2.58498 -0.22391
+2.59932 -0.222744
+2.61737 -0.21986
+2.63792 -0.217012
+2.6518 -0.21531
+2.67292 -0.211322
+2.69242 -0.208046
+2.70593 -0.206326
+2.72694 -0.20112
+2.74969 -0.196002
+2.76288 -0.194366
+2.77971 -0.191118
+2.80569 -0.18289
+2.82481 -0.177534
+2.83762 -0.176016
+2.85698 -0.173063
+2.88233 -0.165418
+2.90751 -0.156343
+2.92236 -0.152274
+2.93484 -0.151542
+2.95743 -0.14985
+2.98222 -0.14547
+3.0069 -0.139639
+3.0315 -0.134555
+3.05603 -0.130407
+3.08051 -0.127268
+3.10496 -0.125194
+3.12938 -0.124181
diff --git a/test/axi/viscous/fadlun b/test/axi/viscous/fadlun
new file mode 100644
index 0000000..7d3dee7
--- /dev/null
+++ b/test/axi/viscous/fadlun
@@ -0,0 +1,10 @@
+#x Fadlun
+25.1277 0.0820564
+30.2905 0.141539
+39.8675 0.297622
+50.1931 0.416587
+59.7792 0.535541
+75.2714 0.699138
+79.7001 0.736332
+199.284 1.70345
+498.74 2.10889
diff --git a/test/axi/viscous/fadlun-cp-100 b/test/axi/viscous/fadlun-cp-100
new file mode 100644
index 0000000..738f6e7
--- /dev/null
+++ b/test/axi/viscous/fadlun-cp-100
@@ -0,0 +1,100 @@
+0.00650221 1.09141
+0.0402099 1.09138
+0.0708118 1.08118
+0.101414 1.07099
+0.138103 1.05063
+0.177828 1.0235
+0.226719 0.989586
+0.269482 0.955678
+0.30606 0.908232
+0.345717 0.86417
+0.379286 0.830272
+0.421938 0.769275
+0.440213 0.742167
+0.470691 0.7015
+0.49809 0.657451
+0.516365 0.630343
+0.531576 0.603237
+0.549851 0.576129
+0.726338 0.271189
+0.741535 0.240698
+0.750631 0.216986
+0.768907 0.189877
+0.784118 0.162772
+0.802393 0.135663
+0.81759 0.105172
+0.835865 0.0780634
+0.893687 -0.020196
+0.951522 -0.115069
+0.969797 -0.142178
+0.988072 -0.169287
+1.00328 -0.196392
+1.02464 -0.220118
+1.06726 -0.287886
+1.1069 -0.335335
+1.12826 -0.359061
+1.20452 -0.443797
+1.22895 -0.464141
+1.25033 -0.481095
+1.29918 -0.525168
+1.32672 -0.535357
+1.35426 -0.545547
+1.3787 -0.562504
+1.40933 -0.565925
+1.43073 -0.579493
+1.45214 -0.589675
+1.46744 -0.593078
+1.49807 -0.596499
+1.51034 -0.593127
+1.541 -0.589775
+1.56553 -0.586417
+1.59616 -0.589838
+1.62072 -0.579707
+1.65135 -0.583128
+1.67895 -0.576387
+1.70659 -0.562874
+1.73727 -0.552751
+1.74648 -0.549375
+1.77409 -0.542634
+1.80172 -0.529122
+1.86004 -0.505485
+1.90917 -0.481839
+1.9368 -0.468326
+1.95831 -0.454806
+1.98286 -0.444676
+2.00742 -0.434546
+2.03197 -0.424415
+2.05347 -0.414282
+2.0811 -0.400769
+2.10872 -0.390642
+2.13635 -0.377129
+2.16705 -0.36362
+2.19466 -0.356879
+2.22229 -0.343366
+2.24684 -0.336622
+2.27752 -0.326498
+2.30514 -0.316371
+2.33276 -0.306245
+2.36037 -0.299504
+2.38799 -0.289377
+2.41866 -0.28264
+2.4432 -0.275895
+2.47387 -0.269158
+2.50148 -0.262417
+2.53215 -0.25568
+2.55976 -0.248939
+2.5843 -0.242194
+2.61189 -0.23884
+2.75911 -0.208532
+2.78669 -0.208563
+2.81429 -0.201822
+2.84495 -0.198471
+2.87562 -0.191733
+2.90628 -0.188382
+2.93387 -0.185027
+2.96453 -0.181676
+2.99519 -0.178324
+3.02279 -0.171583
+3.05342 -0.175004
+3.08408 -0.171652
+3.11474 -0.168301
diff --git a/test/axi/viscous/fadlun-cp-200 b/test/axi/viscous/fadlun-cp-200
new file mode 100644
index 0000000..f4f317d
--- /dev/null
+++ b/test/axi/viscous/fadlun-cp-200
@@ -0,0 +1,100 @@
+#x Re-200
+0.00933136 1.03385
+0.0368966 1.03043
+0.0675123 1.02363
+0.0950636 1.01682
+0.122615 1.01002
+0.150139 0.996445
+0.174584 0.979487
+0.19903 0.962529
+0.220397 0.942189
+0.247907 0.925228
+0.26926 0.901502
+0.290628 0.881162
+0.311981 0.857436
+0.333335 0.83371
+0.354688 0.809983
+0.406505 0.742205
+0.497882 0.606662
+0.577015 0.474518
+0.637859 0.366097
+0.713901 0.227185
+0.774772 0.125536
+0.823484 0.0476033
+0.838681 0.0171121
+0.856956 -0.00999656
+0.872167 -0.0371018
+0.890442 -0.0642104
+0.908718 -0.0913191
+0.923929 -0.118424
+0.942204 -0.145533
+0.96048 -0.172642
+1.10064 -0.369188
+1.12199 -0.392914
+1.14336 -0.413254
+1.16471 -0.43698
+1.18609 -0.453935
+1.20746 -0.474275
+1.25941 -0.508193
+1.3175 -0.542119
+1.37565 -0.559115
+1.4308 -0.562563
+1.45838 -0.562594
+1.48902 -0.562629
+1.51664 -0.552502
+1.54425 -0.545761
+1.57185 -0.53902
+1.5964 -0.532276
+1.62709 -0.518766
+1.65775 -0.515415
+1.69768 -0.491758
+1.72532 -0.478245
+1.75297 -0.461346
+1.78059 -0.45122
+1.8236 -0.42418
+1.85122 -0.414053
+1.8758 -0.397151
+1.90344 -0.383638
+1.92799 -0.373508
+1.95563 -0.359995
+1.98326 -0.346482
+2.01088 -0.336355
+2.03547 -0.319453
+2.06614 -0.312716
+2.09376 -0.302589
+2.12443 -0.295852
+2.14899 -0.285721
+2.17967 -0.275598
+2.21034 -0.26886
+2.23795 -0.26212
+2.26862 -0.255382
+2.29621 -0.252027
+2.32687 -0.248676
+2.35448 -0.241935
+2.38513 -0.238584
+2.41273 -0.235229
+2.44032 -0.231874
+2.47096 -0.231909
+2.50162 -0.228557
+2.53226 -0.228592
+2.55987 -0.221851
+2.59053 -0.218499
+2.63344 -0.215162
+2.68863 -0.208452
+2.73156 -0.201729
+2.75918 -0.191602
+2.78983 -0.18825
+2.81744 -0.18151
+2.84813 -0.171386
+2.87572 -0.168031
+2.9064 -0.157908
+2.9156 -0.157918
+2.9432 -0.151177
+2.97387 -0.14444
+3.00454 -0.137703
+3.03214 -0.134348
+3.05973 -0.130993
+3.09039 -0.127642
+3.12104 -0.12429
+
+
diff --git a/test/axi/viscous/fornberg b/test/axi/viscous/fornberg
new file mode 100644
index 0000000..6d08956
--- /dev/null
+++ b/test/axi/viscous/fornberg
@@ -0,0 +1,6 @@
+#x Fornberg
+99.6247 0.922272
+199.31 1.59949
+497.977 2.20542
+
+
diff --git a/test/axi/isolines.gfv b/test/axi/viscous/isolines.gfv
similarity index 73%
copy from test/axi/isolines.gfv
copy to test/axi/viscous/isolines.gfv
index 39ef52a..c2ab476 100644
--- a/test/axi/isolines.gfv
+++ b/test/axi/viscous/isolines.gfv
@@ -1,9 +1,9 @@
# GfsView 2D
View {
- tx = 0 ty = 0
+ tx = -0.0102258 ty = 2.77268e-05
sx = 1 sy = 1 sz = 1
q0 = 0 q1 = 0 q2 = 0 q3 = 1
- fov = 0.955076
+ fov = 0.895771
r = 0.3 g = 0.4 b = 0.6
res = 1
lc = 0.001
@@ -37,16 +37,30 @@ Isoline {
} {
n = 10
}
-Symmetry {
- r = 0 g = 0 b = 0
+Isoline {
+ r = 0 g = 0.803098 b = 0.139818
shading = Constant
maxlevel = -1
} {
- n.x = 0 n.y = 1 n.z = 0
+ n.x = 0 n.y = 0 n.z = 1
pos = 0
+} U {
+ amin = 1
+ amax = 1
+ cmap = Jet
+} {
+ n = 0 levels = 0
}
Solid {
r = 0 g = 0 b = 0
shading = Constant
maxlevel = -1
}
+Symmetry {
+ r = 0 g = 0 b = 0
+ shading = Constant
+ maxlevel = -1
+} {
+ n.x = 0 n.y = 1 n.z = 0
+ pos = 0
+}
diff --git a/test/axi/viscous/masliyah-1970 b/test/axi/viscous/masliyah-1970
new file mode 100644
index 0000000..9fa5f84
--- /dev/null
+++ b/test/axi/viscous/masliyah-1970
@@ -0,0 +1,5 @@
+20.0094 0.0825769
+49.99 0.91264
+99.9148 1.6556
+
+
diff --git a/test/axi/viscous/viscous.gfs b/test/axi/viscous/viscous.gfs
new file mode 100644
index 0000000..5e1ba23
--- /dev/null
+++ b/test/axi/viscous/viscous.gfs
@@ -0,0 +1,101 @@
+# Title: Viscous flow past a sphere
+#
+# Description:
+#
+# When viscosity is added, a recirculation region develops behind the
+# sphere (Figure \ref{isolines}).
+#
+# \begin{figure}[htbp]
+# \caption{\label{isolines}Viscous flow around a sphere at Reynolds
+# 100. Isolines of the velocity components ($x$ in red, $y$ in
+# blue). The recirculation region is indicated by the green isoline
+# where the value of the horizontal velocity component vanishes.}
+# \begin{center}
+# \includegraphics[width=\hsize]{isolines.eps}
+# \end{center}
+# \end{figure}
+#
+# The length of the recirculation depends on the Reynolds
+# number. Figure \ref{length} plots the results obtained with Gerris
+# as well as previously published results. Published results agree
+# with Gerris for Reynolds numbers smaller than 100. The mismatch for
+# results at Reynolds 200 can be attributed to the coarse mesh used to
+# resolve the wake in the studies of Fornberg \cite{fornberg1988} and
+# Fadlun et al \cite{fadlun2000}.
+#
+# \begin{figure}[htbp]
+# \caption{\label{length}Relative length of the recirculation region
+# as a function of the Reynolds number. The results of Gerris are
+# compared with the results of Masliyah \& Epstein
+# \cite{masliyah1970}, Fornberg \cite{fornberg1988}, Blanco \&
+# Magnaudet \cite{blanco1995}, Fadlun et al \cite{fadlun2000} and
+# Zhang \& Zheng \cite{zhang2007}.}
+# \begin{center}
+# \includegraphics[width=\hsize]{length.eps}
+# \end{center}
+# \end{figure}
+#
+# The pressure profiles are also in good agreement with those reported
+# by Fadlun et al (which also agree with those of Fornberg) (Figure
+# \ref{Cp}).
+#
+# \begin{figure}[htbp]
+# \caption{\label{Cp}Pressure coefficient over the sphere surface at
+# Reynolds numbers 100 and 200.}
+# \begin{center}
+# \includegraphics[width=\hsize]{Cp.eps}
+# \end{center}
+# \end{figure}
+#
+# Author: St\'ephane Popinet
+# Command: sh viscous.sh
+# Version: 1.3.0
+# Required files: viscous.sh cp-12-200 fadlun fadlun-cp-100 fadlun-cp-200 Re-12 zhang blanco-1995 masliyah-1970 isolines.gfv
+# Generated files: length.eps Cp.eps isolines.eps
+#
+
+Define A0 0.5
+Define U0 1.
+
+1 0 GfsAxi GfsBox GfsGEdge {} {
+ Time { end = 100 }
+ PhysicalParams { L = 50 }
+ AdvectionParams { gc = 1 }
+ Refine 4
+ Refine (LEVEL + 1./50.*(x*x + y*y)*(4. - LEVEL))
+ Solid (ellipse (0., 0., A0, A0))
+ SourceViscosity 1./RE
+ Init {} { U = U0 }
+ AdaptGradient { istep = 1 } { cmax = 1e-3 maxlevel = LEVEL } U
+ AdaptGradient { istep = 1 } { cmax = 1e-3 maxlevel = LEVEL } V
+ AdaptFunction { istep = 1 } { cmax = 1e-2 maxlevel = LEVEL } {
+ return (fabs(dx("U"))+fabs(dy("U")))/fabs(U)*ftt_cell_size (cell);
+ }
+ EventStop { step = 0.1 } U 1e-3 DU
+
+# OutputTime { step = 1 } stderr
+# OutputScalarNorm { step = 1 } stderr { v = DU }
+ OutputSimulation { start = end } end-LEVEL-RE.gfs
+ OutputLocation { step = 0.1 } {
+ awk 'BEGIN { t = 2.; oldl = -1.; oldt = 0.; } {
+ if ($1 != t) { t = $1; x1 = $2; u1 = $7; }
+ else {
+ x2 = $2; u2 = $7;
+ if (u1 <= 0. && u2 > 0.) {
+ l = (u1*x2 - u2*x1)/(u1 - u2) - A0;
+ dl = (l - oldl)/(t - oldt);
+ print t, l, dl;
+ fflush (stdout);
+ oldl = l;
+ oldt = t;
+ }
+ x1 = x2; u1 = u2;
+ }
+ }' > l-LEVEL-RE
+ } axis
+}
+GfsBox {
+ left = Boundary { BcDirichlet U U0 }
+ right = BoundaryOutflow
+ bottom = Boundary
+}
diff --git a/test/axi/viscous/viscous.sh b/test/axi/viscous/viscous.sh
new file mode 100644
index 0000000..6d96e31
--- /dev/null
+++ b/test/axi/viscous/viscous.sh
@@ -0,0 +1,50 @@
+if ! $donotrun; then
+ awk 'BEGIN{ for (x = 0.5; x <= 3.; x += 1./256.) print x, 0., 0.;}' > axis
+ for Re in 100; do
+ if gerris2D -DLEVEL=12 -DRE=$Re viscous.gfs; then :
+ else
+ exit 1
+ fi
+ if gfs2oogl2D -c P -o -i < end-12-$Re.gfs | \
+ awk '{print 3.14159265359 - atan2($2,$1),$4*2.}' | \
+ sort -k 1,2 > cp-12-$Re; then :
+ else
+ exit 1
+ fi
+ done
+fi
+
+if echo "Save isolines.eps { format = EPS }" | gfsview-batch2D end-12-100.gfs isolines.gfv; then :
+else
+ exit 1
+fi
+
+if cat <<EOF | gnuplot ; then :
+set term postscript eps color lw 3 solid 20
+set key bottom right
+set pointsize 1.5
+set output 'length.eps'
+set xlabel 'Reynolds number'
+set ylabel 'Recirculation length'
+plot [0:320][0:]'fadlun' t 'Fadlun et al. (2000)', 'fornberg' t 'Fornberg (1988)', 'zhang' t 'Zhang & Zheng (2007)' pt 2, 'blanco-1995' u 1:(\$2/2.) t 'Blanco & Magnaudet (1995)', 'masliyah-1970' u 1:(\$2/2.) t 'Masliyah & Epstein (1970)' pt 8 lt 7, 'Re-12' u 1:3 smooth csplines w l t '' lt 5, 'Re-12' u 1:3 t 'Gerris' lt 5 pt 1
+
+set key top right
+set xlabel 'Angle'
+set ylabel 'Cp'
+set output 'Cp.eps'
+plot 'fadlun-cp-100' u (\$1*180./pi):2 w l t 'Fadlun et al., Re = 100', 'cp-12-100' u (\$1*180./pi):2 w l t 'Gerris, Re = 100', 'fadlun-cp-200' u (\$1*180./pi):2 w l t 'Fadlun et al., Re = 200', 'cp-12-200' u (\$1*180./pi):2 w l t 'Gerris, Re = 200'
+EOF
+else
+ exit 1
+fi
+
+if cat <<EOF | python ; then :
+from check import *
+from sys import *
+if (Curve('cp-12-100',1,2) - Curve('fadlun-cp-100',1,2)).norm2() > 1e-2:
+ print (Curve('cp-12-100',1,2) - Curve('fadlun-cp-100',1,2)).norm2()
+ exit(1)
+EOF
+else
+ exit 1
+fi
diff --git a/test/axi/viscous/zhang b/test/axi/viscous/zhang
new file mode 100644
index 0000000..b9f8bb9
--- /dev/null
+++ b/test/axi/viscous/zhang
@@ -0,0 +1,9 @@
+#x Zhang
+29.8903 0.133929
+40.0366 0.262897
+49.9086 0.386905
+60.0548 0.491071
+80.0731 0.674603
+99.8172 0.848214
+
+
diff --git a/test/template.tex b/test/template.tex
index 874d20b..83c7cdb 100644
--- a/test/template.tex
+++ b/test/template.tex
@@ -59,8 +59,9 @@ branch only.
\input{periodic/periodic.tex}
\input{merging/merging.tex}
-\section{Axisymmetric Euler}
+\section{Axisymmetric}
\input{axi/axi.tex}
+\input{axi/viscous/viscous.tex}
\input{axiadvection/axiadvection.tex}
\input{axiadvection/solid/solid.tex}
diff --git a/test/tests.bib b/test/tests.bib
index a981f71..5298c44 100644
--- a/test/tests.bib
+++ b/test/tests.bib
@@ -29,6 +29,16 @@
edition = {second edition}
}
+ at article{blanco1995,
+ title={The structure of the axisymmetric high-{R}eynolds number flow around an ellipsoidal bubble of fixed shape},
+ author={Blanco, A. and Magnaudet, J.},
+ journal={Physics of Fluids},
+ volume={7},
+ pages={1265},
+ year={1995},
+ publisher={AIP}
+}
+
@PhdThesis{dupont,
author = {F. Dupont},
title = {Comparison of numerical methods for modelling ocean circulation in basins with irregular coasts},
@@ -37,6 +47,25 @@
address = {Montreal}
}
+ at article{fadlun2000,
+ title={Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations},
+ author={Fadlun, EA and Verzicco, R. and Orlandi, P. and Mohd-Yusof, J.},
+ journal={Journal of Computational Physics},
+ volume={161},
+ number={1},
+ pages={35--60},
+ year={2000}
+}
+
+ at Article{fornberg1988,
+ author = {B. Fornberg},
+ title = {Steady viscous flow past a sphere at high {R}eynolds number},
+ journal = {J. Fluid Mech.},
+ year = 1988,
+ volume = 190,
+ pages = 471
+}
+
@article{gerlach2006,
author = {D. Gerlach and G. Tomar and G. Biswas and F. Durst},
title = {Comparison of surface tension methods for surface tension dominant two-phase flows},
@@ -89,6 +118,17 @@
pages = {871-909}
}
+ at article{masliyah1970,
+ title={Numerical study of steady flow past spheroids},
+ author={Masliyah, J.H. and Epstein, N.},
+ journal={Journal of Fluid Mechanics},
+ volume={44},
+ number={03},
+ pages={493--512},
+ year={1970},
+ publisher={Cambridge Univ Press}
+}
+
@Article{minion96,
author = {M. L. Minion},
title = {A Projection Method for Locally Refined Grids},
@@ -185,3 +225,12 @@
number = 2,
pages = {397-420}
}
+
+ at Article{zhang2007,
+ author = {N. Zhang and Z.C. Zheng},
+ title = {An improved direct-forcing immersed-boundary method for finite difference applications},
+ journal = {Journal of Computational Physics},
+ year = 2007,
+ volume = 221,
+ pages = {250-268}
+}
--
Gerris Flow Solver
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