Update refined cylinder2d n=20 grid results

It is unclear why the results changed. However the issue of only the drag error
increasing for higher refinement levels still exists.

4 files changed, 565 insertions, 564 deletions

diff --git a/content.tex b/content.tex
index 22ebadc..a360d2a 100644
--- a/content.tex
+++ b/content.tex
@@ -262,7 +262,7 @@ ist es, außerhalb von etwaigen verfahrensbedingten Übergangsbereichen, jede Po
 \end{figure}

 

 \noindent

-Vorteil gegenüber des Multi-Grid Ansatzes ist hier der weiter reduzierte Speicherbedarf sowie erwartete Einsparungen in der benötigten Rechenzeit. Erkauft werden diese Vorteile durch aufwendigere Kopplung \cite[Kap.~3.1]{Lagrava12} der verschiedenen Teilgitter in den Übergangsbereichen.

+Vorteil gegenüber des Multi-Grid Ansatzes ist hier der weiter reduzierte Speicherbedarf sowie erwartete Einsparungen in der benötigten Rechenzeit. \emph{Erkauft} werden diese Vorteile durch aufwendigere Kopplung \cite[Kap.~3.1]{Lagrava12} der verschiedenen Teilgitter in den Übergangsbereichen.

 

 \subsubsection{Koinzidierende und versetzte Gitter}

 

@@ -1250,14 +1250,14 @@ Das geeignet verfeinerte Gitter liefert demnach in zwei von drei Messwerten eine
 & Uniform & Uniform & Uniform & Verfeinert & Referenzintervall \cite{SchaeferTurek96} \\

 \hline

 \hline

-\(\widehat{c_w}\) & \num{3.23526} & \num{3.24441} & \num{3.24897} & \num{3.19928} & \([\num[round-mode=off]{3.22},\ \num[round-mode=off]{3.24}]\) \\

-\(|\widehat{c_w}-\num[round-mode=off]{3.23}|\) & \num{0.00526} & \num{0.01441} & \num{0.01897} & \num{0.03072} & [\num[round-mode=off]{0}, \num[round-mode=off]{0.01}] \\

+\(\widehat{c_w}\) & \num{3.23526} & \num{3.24441} & \num{3.24897} & \num{3.20043} & \([\num[round-mode=off]{3.22},\ \num[round-mode=off]{3.24}]\) \\

+\(|\widehat{c_w}-\num[round-mode=off]{3.23}|\) & \num{0.00526} & \num{0.01441} & \num{0.01897} & \num{0.02957} & [\num[round-mode=off]{0}, \num[round-mode=off]{0.01}] \\

 \hline

-\(\widehat{c_a}\) & \num{1.00194} & \num{1.01377} & \num{1.02121} & \num{0.995577} & \([\num[round-mode=off]{0.99},\ \num[round-mode=off]{1.01}]\) \\

-\(|\widehat{c_a}-\num[round-mode=off]{1.0}|\) & \num{0.00194} & \num{0.01377} & \num{0.02121} & \num{0.004423} & [\num[round-mode=off]{0}, \num[round-mode=off]{0.01}]  \\

+\(\widehat{c_a}\) & \num{1.00194} & \num{1.01377} & \num{1.02121} & \num{0.995584} & \([\num[round-mode=off]{0.99},\ \num[round-mode=off]{1.01}]\) \\

+\(|\widehat{c_a}-\num[round-mode=off]{1.0}|\) & \num{0.00194} & \num{0.01377} & \num{0.02121} & \num{0.004416} & [\num[round-mode=off]{0}, \num[round-mode=off]{0.01}]  \\

 \hline

-\(\Delta P\) & \num{2.49969} & \num{2.50671} & \num{2.44354} & \num{2.46411} & \([\num[round-mode=off]{2.46},\ \num[round-mode=off]{2.5}]\)  \\

-\(|\Delta P-\num[round-mode=off]{2.48}|\) & \num{0.01969} & \num{0.02671} & \num{0.03646} & \num{0.01589} & [\num[round-mode=off]{0}, \num[round-mode=off]{0.02}] \\

+\(\Delta P\) & \num{2.49969} & \num{2.50671} & \num{2.44354} & \num{2.46461} & \([\num[round-mode=off]{2.46},\ \num[round-mode=off]{2.5}]\)  \\

+\(|\Delta P-\num[round-mode=off]{2.48}|\) & \num{0.01969} & \num{0.02671} & \num{0.03646} & \num{0.01539} & [\num[round-mode=off]{0}, \num[round-mode=off]{0.02}] \\

 \hline

 \hline

 \(N=\) & \num{160} & \num{80} & \num{48} & \num{20} (max: \num{160}) & \\

@@ -1267,7 +1267,6 @@ Knotenanzahl & \num{2298014} & \num{576758} & \num{207862} & \num{208031} & \\
 \label{tab:cylinder2dHighResComparison}

 \end{table}

 

-

 Da alle vier getesteten Gitter gute Übereinstimmung zu den Referenzdaten von Schäfer und Turek aufweisen, fällt der Vorteil der Gitterverfeinerung im Allgemeinen jedoch geringer aus, als noch im Vergleich der niedrig aufgelösten Gitter aus Abbildung~\ref{fig:CylinderOptimizedGridComparison} und Tabelle~\ref{tab:cylinder2dComparison}. Darüber hinaus liegt die Knotenanzahl des betrachteten \(N=160\) Gitters weit oberhalb der maximalen referenzstiftenden Knotenzahlen \cite[Tabelle~4]{SchaeferTurek96}, so dass wir hier an die Grenzen der Aussagekraft von Fehlern bezüglich dieser Werte stoßen.

 

 \bigskip

diff --git a/img/cylinder2d_high_res_drag_comparison.tikz b/img/cylinder2d_high_res_drag_comparison.tikz
index 927fa1a..e847f47 100644
--- a/img/cylinder2d_high_res_drag_comparison.tikz
+++ b/img/cylinder2d_high_res_drag_comparison.tikz
@@ -19,6 +19,7 @@
 	y tick label style={/pgf/number format/.cd, use comma}
 ]
 
+
 \addplot[color=black]{3.23};
 \addlegendentry {Gemittelte Referenzlösung \(c_\text{Wmax} := \num{3.23}\)};
 \addplot[color=blue!50!white,thin,densely dashed] table [x expr=\thisrow{time}, y=drag] {\uniformHigh};
diff --git a/img/cylinder2d_high_res_lift_deltap_comparison.tikz b/img/cylinder2d_high_res_lift_deltap_comparison.tikz
index 4b42257..9aee420 100644
--- a/img/cylinder2d_high_res_lift_deltap_comparison.tikz
+++ b/img/cylinder2d_high_res_lift_deltap_comparison.tikz
@@ -43,6 +43,7 @@
 	y tick label style={/pgf/number format/.cd, use comma}
 ]
 
+
 \addplot[color=black]{2.48};
 \addlegendentry {Gemittelte Referenzlösung \(\Delta P := \num{2.48}\)};
 \addplot[color=blue!50!white,thin,densely dashed] table [x expr=\thisrow{time}, y=deltap] {\uniformHigh};
diff --git a/img/data/cylinder2d_optimized_grid_n20_re100_drag_lift_deltap.csv b/img/data/cylinder2d_optimized_grid_n20_re100_drag_lift_deltap.csv
index 9950110..a1d74c2 100644
--- a/img/data/cylinder2d_optimized_grid_n20_re100_drag_lift_deltap.csv
+++ b/img/data/cylinder2d_optimized_grid_n20_re100_drag_lift_deltap.csv
@@ -1,12 +1,12 @@
 time,drag,lift,deltap
 0,0,0,0
-0.00125,6.76986e-07,-6.87996e-09,4.29096e-07
-0.0025,8.28109e-06,-2.69139e-08,5.04618e-06
-0.00375,2.5731e-05,-6.00146e-08,1.54492e-05
-0.005,5.30404e-05,-1.15532e-07,3.1504e-05
-0.00625,9.04374e-05,-1.77196e-07,5.32446e-05
+0.00125,6.76986e-07,-6.87987e-09,4.29095e-07
+0.0025,8.28109e-06,-2.69143e-08,5.04618e-06
+0.00375,2.5731e-05,-6.00143e-08,1.54492e-05
+0.005,5.30404e-05,-1.15533e-07,3.1504e-05
+0.00625,9.04374e-05,-1.77195e-07,5.32446e-05
 0.0075,0.000138246,-2.6031e-07,8.07773e-05
-0.00875,0.000196726,-3.55861e-07,0.000114177
+0.00875,0.000196726,-3.55863e-07,0.000114177
 0.01,0.000266097,-4.63887e-07,0.0001535
 0.01125,0.000346556,-5.89186e-07,0.000198798
 0.0125,0.000438287,-7.22734e-07,0.000250115
@@ -38,7 +38,7 @@ time,drag,lift,deltap
 0.045,0.00733316,-8.43983e-06,0.00385911
 0.04625,0.00776979,-8.87305e-06,0.00408025
 0.0475,0.00822079,-9.31182e-06,0.00430824
-0.04875,0.00868777,-9.76183e-06,0.00454403
+0.04875,0.00868777,-9.76182e-06,0.00454403
 0.05,0.00917372,-1.02161e-05,0.0047893
 0.05125,0.00967448,-1.06766e-05,0.00504145
 0.0525,0.0101879,-1.11455e-05,0.00529921
@@ -56,7 +56,7 @@ time,drag,lift,deltap
 0.0675,0.0173981,-1.70411e-05,0.00886425
 0.06875,0.0180808,-1.75502e-05,0.00919719
 0.07,0.0187768,-1.80652e-05,0.00953605
-0.07125,0.0194858,-1.85807e-05,0.00988067
+0.07125,0.0194858,-1.85806e-05,0.00988067
 0.0725,0.0202082,-1.90949e-05,0.0102312
 0.07375,0.020944,-1.96106e-05,0.0105877
 0.075,0.0216932,-2.0127e-05,0.0109501
@@ -124,10 +124,10 @@ time,drag,lift,deltap
 0.1525,0.0938466,-1.2628e-05,0.0445431
 0.15375,0.0954117,-1.07678e-05,0.0452631
 0.155,0.0969896,-8.79564e-06,0.0459892
-0.15625,0.0985805,-6.70458e-06,0.0467216
+0.15625,0.0985805,-6.70459e-06,0.0467216
 0.1575,0.100184,-4.49376e-06,0.0474603
 0.15875,0.1018,-2.15584e-06,0.0482051
-0.16,0.103428,3.08361e-07,0.0489555
+0.16,0.103428,3.08363e-07,0.0489555
 0.16125,0.105067,2.90915e-06,0.0497115
 0.1625,0.106716,5.64455e-06,0.0504729
 0.16375,0.108378,8.52324e-06,0.0512403
@@ -1050,553 +1050,553 @@ time,drag,lift,deltap
 1.31,3.16648,0.905774,2.40963
 1.31125,3.17839,0.963591,2.42517
 1.3125,3.18846,0.986761,2.44009
-1.31375,3.1953,0.974651,2.45231
+1.31375,3.19529,0.974651,2.45231
 1.315,3.19798,0.928016,2.46018
 1.31625,3.19625,0.848744,2.46275
 1.3175,3.19049,0.739674,2.45984
-1.31875,3.18161,0.604677,2.45198
-1.32,3.17087,0.44831,2.44029
+1.31875,3.1816,0.604677,2.45198
+1.32,3.17086,0.44831,2.44029
 1.32125,3.15972,0.275758,2.42633
-1.3225,3.14965,0.0928415,2.41195
-1.32375,3.14196,-0.0943307,2.39905
-1.325,3.13767,-0.27928,2.38942
-1.32625,3.13734,-0.455545,2.38443
-1.3275,3.14105,-0.61686,2.38486
-1.32875,3.1483,-0.757362,2.39073
-1.33,3.15811,-0.872002,2.40128
-1.33125,3.16913,-0.956617,2.415
-1.3325,3.17973,-1.00824,2.42989
-1.33375,3.18832,-1.02518,2.44373
-1.335,3.19359,-1.00701,2.45453
-1.33625,3.19479,-0.954608,2.46081
-1.3375,3.19176,-0.869933,2.46177
-1.33875,3.185,-0.75594,2.45737
-1.34,3.17547,-0.616594,2.44823
-1.34125,3.16455,-0.456484,2.43561
-1.3425,3.15374,-0.28094,2.42115
-1.34375,3.14451,-0.0958866,2.40675
-1.345,3.13811,0.092457,2.39432
-1.34625,3.13544,0.277423,2.38558
-1.3475,3.13692,0.452492,2.38182
-1.34875,3.14244,0.61128,2.38368
-1.35,3.15137,0.747914,2.39103
-1.35125,3.16258,0.857455,2.40291
-1.3525,3.17454,0.935843,2.41761
-1.35375,3.18553,0.98042,2.433
-1.355,3.19398,0.989773,2.44685
-1.35625,3.19866,0.963826,2.45719
-1.3575,3.19892,0.903863,2.46264
-1.35875,3.19473,0.812141,2.46256
-1.36,3.18672,0.691977,2.45704
-1.36125,3.17602,0.547559,2.44692
-1.3625,3.16407,0.383718,2.43355
-1.36375,3.15247,0.205926,2.4187
-1.365,3.14273,0.0201476,2.40433
-1.36625,3.13621,-0.167361,2.39242
-1.3675,3.13402,-0.350094,2.38478
-1.36875,3.13672,-0.521664,2.3827
-1.37,3.14401,-0.675943,2.3866
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-1.375,3.18687,-1.02182,2.43769
-1.37625,3.19393,-1.02511,2.4504
-1.3775,3.19769,-0.993338,2.45963
-1.37875,3.19755,-0.927867,2.46411
-1.38,3.19336,-0.831018,2.46318
-1.38125,3.18558,-0.706191,2.45693
-1.3825,3.17512,-0.557648,2.44611
-1.38375,3.1632,-0.39025,2.43199
-1.385,3.15124,-0.209695,2.41631
-1.38625,3.14099,-0.0220268,2.40117
-1.3875,3.13434,0.166271,2.38894
-1.38875,3.13275,0.348535,2.38165
-1.39,3.1365,0.518325,2.38042
-1.39125,3.14459,0.669376,2.38517
-1.3925,3.1554,0.796206,2.39497
-1.39375,3.16723,0.894152,2.40831
-1.395,3.17854,0.95968,2.42331
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-1.405,3.16303,0.317008,2.4301
-1.40625,3.1515,0.135005,2.4149
-1.4075,3.1422,-0.0526215,2.40083
-1.40875,3.13696,-0.239465,2.39018
-1.41,3.13671,-0.418992,2.3846
-1.41125,3.14129,-0.584915,2.38485
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