From 8221184819a52f6a83d64f8f03559778ec9f29f2 Mon Sep 17 00:00:00 2001
From: Adrian Kummerlaender
Date: Mon, 4 Feb 2019 16:50:35 +0100
Subject: Redo remaining cylinder2d plots

---
 content.tex                                        |    22 +-
 ...r2d_improved_grid_n20_re100_16s_knudsen.gnuplot |    18 +
 ...der2d_low_resolution_outflow_refine_60s.gnuplot |    13 -
 ...w_resolution_outflow_refine_60s_knudsen.gnuplot |    14 -
 ..._resolution_outflow_refine_n5_re100_16s.gnuplot |    19 +
 ...der2d_optimized_low_resolution_grid_60s.gnuplot |    27 -
 ...timized_low_resolution_grid_60s_knudsen.gnuplot |    23 -
 ...der2d_optimized_refinement_n5_re100_16s.gnuplot |    33 +
 ...timized_refinement_n5_re100_16s_knudsen.gnuplot |    32 +
 ...inder2d_single_refinement_n20_re100_16s.gnuplot |    13 +
 ...single_refinement_n20_re100_16s_knudsen.gnuplot |    14 +
 ...r2d_unoptimized_low_resolution_grid_60s.gnuplot |    11 -
 img/cylinder2d_unrefined_n12_re100_16s.gnuplot     |    11 +
 img/cylinder2d_unrefined_n20_re100_16s.gnuplot     |     9 +
 ...inder2d_unrefined_n20_re100_16s_knudsen.gnuplot |    10 +
 img/cylinder2d_unrefined_n40_re100_16s.gnuplot     |    12 +
 ...inder2d_unrefined_n40_re100_16s_knudsen.gnuplot |    13 +
 ...ylinder2d_improved_grid_twice_refined_60s_0.csv | 46977 -------------------
 ...ylinder2d_improved_grid_twice_refined_60s_1.csv | 39593 ----------------
 ...ylinder2d_improved_grid_twice_refined_60s_2.csv | 24515 ----------
 ..._grid_twice_refined_resolution_halved_60s_0.csv | 11945 -----
 ..._grid_twice_refined_resolution_halved_60s_1.csv | 10193 ----
 ..._grid_twice_refined_resolution_halved_60s_2.csv |  6434 ---
 ...der2d_laminar_single_level_refinement_60s_0.csv | 37745 ---------------
 ...der2d_laminar_single_level_refinement_60s_1.csv | 27655 -----------
 ...inder2d_low_resolution_outflow_refine_60s_0.csv |   452 -
 ...inder2d_low_resolution_outflow_refine_60s_1.csv |  2243 -
 ...ow_resolution_outflow_refine_n5_re100_16s_0.csv |   936 +
 ...ow_resolution_outflow_refine_n5_re100_16s_1.csv |   302 +
 ...ow_resolution_outflow_refine_n5_re100_16s_2.csv |  2373 +
 img/data/cylinder2d_optimized_grid_n11_60s_0.csv   | 12807 -----
 img/data/cylinder2d_optimized_grid_n11_60s_1.csv   | 12284 -----
 img/data/cylinder2d_optimized_grid_n11_60s_2.csv   |  1002 -
 img/data/cylinder2d_optimized_grid_n11_60s_3.csv   |  7595 ---
 ...inder2d_optimized_low_resolution_grid_60s_0.csv |  1929 -
 ...inder2d_optimized_low_resolution_grid_60s_1.csv |  1000 -
 ...inder2d_optimized_low_resolution_grid_60s_2.csv |   452 -
 ...inder2d_optimized_low_resolution_grid_60s_3.csv |  2140 -
 ...inder2d_optimized_low_resolution_grid_60s_4.csv |  1813 -
 ...inder2d_optimized_refinement_n5_re100_16s_0.csv |  1504 +
 ...inder2d_optimized_refinement_n5_re100_16s_1.csv |   936 +
 ...inder2d_optimized_refinement_n5_re100_16s_2.csv |   302 +
 ...inder2d_optimized_refinement_n5_re100_16s_3.csv |  6486 +++
 ...inder2d_optimized_refinement_n5_re100_16s_4.csv |  2639 ++
 ...inder2d_optimized_refinement_n5_re100_16s_5.csv |  1593 +
 .../cylinder2d_single_level_refinement_60s_0.csv   | 27655 -----------
 .../cylinder2d_single_level_refinement_60s_1.csv   | 37745 ---------------
 ...inder2d_unoptimized_low_resolution_grid_60s.csv |  7327 ---
 img/data/cylinder2d_unrefined_60s.csv              | 36533 --------------
 img/data/cylinder2d_unrefined_n12_re100_16s.csv    | 13501 ++++++
 ...inder2d_improved_grid_n20_re100_16s_knudsen.pdf |   Bin 96793 -> 96793 bytes
 ...ylinder2d_low_resolution_outflow_refine_60s.pdf |   Bin 91696 -> 0 bytes
 ...d_low_resolution_outflow_refine_60s_knudsen.pdf |   Bin 60467 -> 0 bytes
 ..._low_resolution_outflow_refine_n5_re100_16s.pdf |   Bin 0 -> 95974 bytes
 ...ylinder2d_optimized_low_resolution_grid_60s.pdf |   Bin 141809 -> 0 bytes
 ...d_optimized_low_resolution_grid_60s_knudsen.pdf |   Bin 44683 -> 0 bytes
 ...ylinder2d_optimized_refinement_n5_re100_16s.pdf |   Bin 0 -> 264964 bytes
 ...d_optimized_refinement_n5_re100_16s_knudsen.pdf |   Bin 0 -> 91235 bytes
 .../cylinder2d_single_refinement_n20_re100_16s.pdf |   Bin 588263 -> 588263 bytes
 ...r2d_single_refinement_n20_re100_16s_knudsen.pdf |   Bin 98478 -> 98478 bytes
 ...inder2d_unoptimized_low_resolution_grid_60s.pdf |   Bin 144259 -> 0 bytes
 img/static/cylinder2d_unrefined_n12_re100_16s.pdf  |   Bin 0 -> 230847 bytes
 img/static/cylinder2d_unrefined_n20_re100_16s.pdf  |   Bin 305191 -> 305191 bytes
 .../cylinder2d_unrefined_n20_re100_16s_knudsen.pdf |   Bin 80479 -> 80479 bytes
 img/static/cylinder2d_unrefined_n40_re100_16s.pdf  |   Bin 895747 -> 895747 bytes
 .../cylinder2d_unrefined_n40_re100_16s_knudsen.pdf |   Bin 84684 -> 84684 bytes
 ...ylinder2d_low_resolution_outflow_refine_60s.png |   Bin 30415 -> 0 bytes
 ...d_low_resolution_outflow_refine_60s_knudsen.png |   Bin 16849 -> 0 bytes
 ..._low_resolution_outflow_refine_n5_re100_16s.png |   Bin 0 -> 36168 bytes
 ...ylinder2d_optimized_low_resolution_grid_60s.png |   Bin 67943 -> 0 bytes
 ...d_optimized_low_resolution_grid_60s_knudsen.png |   Bin 23980 -> 0 bytes
 ...ylinder2d_optimized_refinement_n5_re100_16s.png |   Bin 0 -> 146251 bytes
 ...d_optimized_refinement_n5_re100_16s_knudsen.png |   Bin 0 -> 55477 bytes
 ...inder2d_unoptimized_low_resolution_grid_60s.png |   Bin 70405 -> 0 bytes
 img/tmp/cylinder2d_unrefined_n12_re100_16s.png     |   Bin 0 -> 133813 bytes
 75 files changed, 30769 insertions(+), 358131 deletions(-)
 create mode 100644 img/cylinder2d_improved_grid_n20_re100_16s_knudsen.gnuplot
 delete mode 100644 img/cylinder2d_low_resolution_outflow_refine_60s.gnuplot
 delete mode 100644 img/cylinder2d_low_resolution_outflow_refine_60s_knudsen.gnuplot
 create mode 100644 img/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.gnuplot
 delete mode 100644 img/cylinder2d_optimized_low_resolution_grid_60s.gnuplot
 delete mode 100644 img/cylinder2d_optimized_low_resolution_grid_60s_knudsen.gnuplot
 create mode 100644 img/cylinder2d_optimized_refinement_n5_re100_16s.gnuplot
 create mode 100644 img/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.gnuplot
 create mode 100644 img/cylinder2d_single_refinement_n20_re100_16s.gnuplot
 create mode 100644 img/cylinder2d_single_refinement_n20_re100_16s_knudsen.gnuplot
 delete mode 100644 img/cylinder2d_unoptimized_low_resolution_grid_60s.gnuplot
 create mode 100644 img/cylinder2d_unrefined_n12_re100_16s.gnuplot
 create mode 100644 img/cylinder2d_unrefined_n20_re100_16s.gnuplot
 create mode 100644 img/cylinder2d_unrefined_n20_re100_16s_knudsen.gnuplot
 create mode 100644 img/cylinder2d_unrefined_n40_re100_16s.gnuplot
 create mode 100644 img/cylinder2d_unrefined_n40_re100_16s_knudsen.gnuplot
 delete mode 100644 img/data/cylinder2d_improved_grid_twice_refined_60s_0.csv
 delete mode 100644 img/data/cylinder2d_improved_grid_twice_refined_60s_1.csv
 delete mode 100644 img/data/cylinder2d_improved_grid_twice_refined_60s_2.csv
 delete mode 100644 img/data/cylinder2d_improved_grid_twice_refined_resolution_halved_60s_0.csv
 delete mode 100644 img/data/cylinder2d_improved_grid_twice_refined_resolution_halved_60s_1.csv
 delete mode 100644 img/data/cylinder2d_improved_grid_twice_refined_resolution_halved_60s_2.csv
 delete mode 100644 img/data/cylinder2d_laminar_single_level_refinement_60s_0.csv
 delete mode 100644 img/data/cylinder2d_laminar_single_level_refinement_60s_1.csv
 delete mode 100644 img/data/cylinder2d_low_resolution_outflow_refine_60s_0.csv
 delete mode 100644 img/data/cylinder2d_low_resolution_outflow_refine_60s_1.csv
 create mode 100644 img/data/cylinder2d_low_resolution_outflow_refine_n5_re100_16s_0.csv
 create mode 100644 img/data/cylinder2d_low_resolution_outflow_refine_n5_re100_16s_1.csv
 create mode 100644 img/data/cylinder2d_low_resolution_outflow_refine_n5_re100_16s_2.csv
 delete mode 100644 img/data/cylinder2d_optimized_grid_n11_60s_0.csv
 delete mode 100644 img/data/cylinder2d_optimized_grid_n11_60s_1.csv
 delete mode 100644 img/data/cylinder2d_optimized_grid_n11_60s_2.csv
 delete mode 100644 img/data/cylinder2d_optimized_grid_n11_60s_3.csv
 delete mode 100644 img/data/cylinder2d_optimized_low_resolution_grid_60s_0.csv
 delete mode 100644 img/data/cylinder2d_optimized_low_resolution_grid_60s_1.csv
 delete mode 100644 img/data/cylinder2d_optimized_low_resolution_grid_60s_2.csv
 delete mode 100644 img/data/cylinder2d_optimized_low_resolution_grid_60s_3.csv
 delete mode 100644 img/data/cylinder2d_optimized_low_resolution_grid_60s_4.csv
 create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_16s_0.csv
 create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_16s_1.csv
 create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_16s_2.csv
 create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_16s_3.csv
 create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_16s_4.csv
 create mode 100644 img/data/cylinder2d_optimized_refinement_n5_re100_16s_5.csv
 delete mode 100644 img/data/cylinder2d_single_level_refinement_60s_0.csv
 delete mode 100644 img/data/cylinder2d_single_level_refinement_60s_1.csv
 delete mode 100644 img/data/cylinder2d_unoptimized_low_resolution_grid_60s.csv
 delete mode 100644 img/data/cylinder2d_unrefined_60s.csv
 create mode 100644 img/data/cylinder2d_unrefined_n12_re100_16s.csv
 delete mode 100644 img/static/cylinder2d_low_resolution_outflow_refine_60s.pdf
 delete mode 100644 img/static/cylinder2d_low_resolution_outflow_refine_60s_knudsen.pdf
 create mode 100644 img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdf
 delete mode 100644 img/static/cylinder2d_optimized_low_resolution_grid_60s.pdf
 delete mode 100644 img/static/cylinder2d_optimized_low_resolution_grid_60s_knudsen.pdf
 create mode 100644 img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdf
 create mode 100644 img/static/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.pdf
 delete mode 100644 img/static/cylinder2d_unoptimized_low_resolution_grid_60s.pdf
 create mode 100644 img/static/cylinder2d_unrefined_n12_re100_16s.pdf
 delete mode 100644 img/tmp/cylinder2d_low_resolution_outflow_refine_60s.png
 delete mode 100644 img/tmp/cylinder2d_low_resolution_outflow_refine_60s_knudsen.png
 create mode 100644 img/tmp/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.png
 delete mode 100644 img/tmp/cylinder2d_optimized_low_resolution_grid_60s.png
 delete mode 100644 img/tmp/cylinder2d_optimized_low_resolution_grid_60s_knudsen.png
 create mode 100644 img/tmp/cylinder2d_optimized_refinement_n5_re100_16s.png
 create mode 100644 img/tmp/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.png
 delete mode 100644 img/tmp/cylinder2d_unoptimized_low_resolution_grid_60s.png
 create mode 100644 img/tmp/cylinder2d_unrefined_n12_re100_16s.png

diff --git a/content.tex b/content.tex
index 932e914..ef1ae00 100644
--- a/content.tex
+++ b/content.tex
@@ -1035,34 +1035,38 @@ Insgesamt war unter dieser formaleren Analyse unsere intuitive Wahl des in Abbil
 \caption{Verbesserte Verfeinerungsstruktur um den Zylinder}
 \end{figure}
 
-Typischerweise sind LBM-Simulationen des umströmten Zylinders für wirbelbildende Reynolds-Zahlen bei kleineren Auflösungen empfindlich gegenüber Verteilungsdivergenz im Ausflussbereich. Dies deutet sich auch bei noch ausreichender Auslösung in den Verfeinerungsfaktoren des Ausgangsbereiches an. So divergiert ein uniform mit \(N=5\) aufgelöstes Gitter mit den verwendeten Parametern und Randbedingungen schon nach wenigen Schritten. Es wäre vorteilhaft, wenn sich dieses Problem unter Einsatz möglichst weniger zusätzlicher Gitterknoten beheben ließe -- etwa durch Verfeinerung des Ausflussbereiches. Und tatsächlich genügt schon die Verfeinerung eines schmalen Stücks des Ausgangsbereiches zur Stabilisierung der Simulation bei dieser niedrigen Auflösung. In Abbildung~\ref{fig:CylinderOptimizedGridN5} sehen wir den Geschwindigkeitsplot eines solchen Gitters.
+Typischerweise sind LBM-Simulationen des umströmten Zylinders für wirbelbildende Reynolds-Zahlen bei kleineren Auflösungen empfindlich gegenüber Verteilungsdivergenz im Ausflussbereich. Dies deutet sich auch bei noch ausreichender Auslösung in den Verfeinerungsfaktoren des Ausgangsbereiches an. So divergiert ein uniform mit \(N=5\) aufgelöstes Gitter mit den verwendeten Parametern und Randbedingungen schon nach wenigen Schritten. Es wäre vorteilhaft, wenn sich dieses Problem unter Einsatz möglichst weniger zusätzlicher Gitterknoten beheben ließe -- etwa durch Verfeinerung des Ausflussbereiches.
+Und tatsächlich genügt schon die Verfeinerung eines schmalen Stücks des Ausgangsbereiches zur Stabilisierung der Simulation bei dieser niedrigen Auflösung. In Abbildung~\ref{fig:CylinderOptimizedGridN5} sehen wir den Geschwindigkeitsplot eines solchen Gitters.
+
+\bigskip
+
+Dieses Beispiel gewinnt insbesondere an Eindruck, wenn wir die Gesamtanzahl der Gitterzellen mit den für ein stabiles uniformes Gitter benötigten Zellen vergleichen: Während das im Ausgang verfeinerte Gitter nur 3608 aktive Zellen beinhaltet, benötigt ein stabiles uniformes Gitter eine Auflösung von mindestens \(N=12\), was 13500 Zellen entspricht. Interessieren wir uns an dieser Stelle also nur für ein subjektiv korrektes und nicht-divergentes Strömungsbild, so ermöglicht uns Gitterverfeinerung ein Auskommen mit nur etwa einem Viertel der für ein unverfeinertes Gitter benötigten Zellen.
 
 \begin{figure}[h]
 \begin{adjustbox}{center}
-\includegraphics[width=1.2\textwidth]{img/static/cylinder2d_low_resolution_outflow_refine_60s.pdf}
+\includegraphics[width=1.2\textwidth]{img/static/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.pdf}
 \end{adjustbox}
 \caption{Stabile Zylinderumströmung mit \(N=5\) durch Ausgangsverfeinerung}
 \label{fig:CylinderOptimizedGridN5}
 \end{figure}
 
-Dieses Beispiel gewinnt insbesondere an Eindruck, wenn wir die Gesamtanzahl der Gitterzellen mit den für ein stabiles uniformes Gitter benötigten Zellen vergleichen: Während das im Ausgang verfeinerte Gitter nur 2693 aktive Zellen beinhaltet, benötigt ein stabiles uniformes Gitter eine Auflösung von \(N=9\), was 7326 Zellen entspricht. Interessieren wir uns an dieser Stelle also nur für ein subjektiv korrektes und nicht-divergentes Strömungsbild, so ermöglicht uns Gitterverfeinerung ein Auskommen mit nur knapp einem Drittel der für ein unverfeinertes Gitter benötigten Zellen.
+Alternativ ist es möglich über das Festhalten der Anzahl der Freiheitsgrade, d.h. der Knotenanzahl, beschränkte Rechenressourcen besser auf die zu simulierende Strömungssituation anzupassen. Beispielsweise fällt auf, dass der zentrale Zylinder in Abbildung~\ref{fig:CylinderOptimizedGridN5} nur sehr grob modelliert wird. Entsprechend wollen wir versuchen, bei Einschränkung auf die Anzahl der Gitterknoten eines uniformen Gitters mit \(N=12\), ein besseres Gitter zu erzeugen.
 
 \begin{figure}[h]
 \begin{adjustbox}{center}
-\includegraphics[width=1.2\textwidth]{img/static/cylinder2d_unoptimized_low_resolution_grid_60s.pdf}
+\includegraphics[width=1.2\textwidth]{img/static/cylinder2d_unrefined_n12_re100_16s.pdf}
 \end{adjustbox}
 \begin{adjustbox}{center}
-\includegraphics[width=1.2\textwidth]{img/static/cylinder2d_optimized_low_resolution_grid_60s.pdf}
+\includegraphics[width=1.2\textwidth]{img/static/cylinder2d_optimized_refinement_n5_re100_16s.pdf}
 \end{adjustbox}
 \caption{Vergleich von uniform und problembezogen verteilten Freiheitsgraden}
 \label{fig:CylinderOptimizedGridComparison}
 \end{figure}
 
-Alternativ ist es möglich über das Festhalten der Anzahl der Freiheitsgrade, d.h. der Knotenanzahl, beschränkte Rechenressourcen besser auf die zu simulierende Strömungssituation anzupassen. Beispielsweise fällt auf, dass der zentrale Zylinder in Abbildung~\ref{fig:CylinderOptimizedGridN5} nur sehr grob modelliert wird. Entsprechend wollen wir versuchen, bei Einschränkung auf die Anzahl der Gitterknoten eines uniformen Gitters mit \(N=9\), ein besseres Gitter zu erzeugen.
-
-Wir sehen das Geschwindigkeitsbild dieser Bemühungen in Abbildung~\ref{fig:CylinderOptimizedGridComparison}. Die dort dargestellten Gitter beinhalten beide jeweils insgesamt \(7327\pm2\) Zellen. Der kleine Unterschied in der Knotenanzahl ist dabei der Einschränkung auf quaderförmige Gitter geschuldet, welche eine exakte Fixierung der Knotenanzahl erschwert.
+\newpage
+Wir sehen das Geschwindigkeitsbild dieser Bemühungen in Abbildung~\ref{fig:CylinderOptimizedGridComparison}. Die dort dargestellten Gitter beinhalten beide jeweils maximal 13500 Zellen. Der kleine Unterschied in der Knotenanzahl ist dabei der Einschränkung auf quaderförmige Gitter geschuldet, welche eine exakte Fixierung der Knotenanzahl erschwert.
 
-Klar zu erkennen ist die in der verfeinerten Variante deutlich bessere Diskretisierung des Zylinders durch Konzentration der verfügbaren Gitterknoten in dessen Umfeld. Eine formalere Analyse der Qualität dieses optimierten Gitters erwartet uns im nachfolgenden Unterkapitel.
+Klar zu erkennen ist die in der verfeinerten Variante deutlich bessere Diskretisierung des Zylinders durch Konzentration der verfügbaren Gitterknoten in dessen Umfeld. Auch liegt dem Ausfluss des verfeinerten Gitters die Divergenz ferner als dem Ausfluss des uniformen Gitters, an welchem sich schon Artefakte abzeichnen. Eine formalere Analyse der Qualität dieses optimierten Gitters erwartet uns im nachfolgenden Unterkapitel.
 
 \bigskip
 
diff --git a/img/cylinder2d_improved_grid_n20_re100_16s_knudsen.gnuplot b/img/cylinder2d_improved_grid_n20_re100_16s_knudsen.gnuplot
new file mode 100644
index 0000000..1ad5e8b
--- /dev/null
+++ b/img/cylinder2d_improved_grid_n20_re100_16s_knudsen.gnuplot
@@ -0,0 +1,18 @@
+plotname = "cylinder2d_improved_grid_n20_re100_16s_knudsen"
+knudsen = 0.000288675
+
+load 'common/knudsen_fluid.gnuplot'
+
+plot 'data/cylinder2d_improved_grid_twice_refined_n20_re100_16s_0.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 1.3 notitle,\
+     'data/cylinder2d_improved_grid_twice_refined_n20_re100_16s_2.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_improved_grid_twice_refined_n20_re100_16s_1.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.3 notitle,\
+
+load 'common/knudsen_wrapper.gnuplot'
+
+set obj 1 rect from 0.5,0.05 to 8.51,4.05
+set obj 1 fillstyle empty border -1 front lw 1
+
+set obj 2 rect from 1,1.08 to 5.01,3.08
+set obj 2 fillstyle empty border -1 front lw 1
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_low_resolution_outflow_refine_60s.gnuplot b/img/cylinder2d_low_resolution_outflow_refine_60s.gnuplot
deleted file mode 100644
index 42ec009..0000000
--- a/img/cylinder2d_low_resolution_outflow_refine_60s.gnuplot
+++ /dev/null
@@ -1,13 +0,0 @@
-plotname = "cylinder2d_low_resolution_outflow_refine_60s"
-
-load 'common/velocity_fluid.gnuplot'
-
-plot 'data/cylinder2d_low_resolution_outflow_refine_60s_1.csv' using ($6+0.05):($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 5.3 notitle,\
-     'data/cylinder2d_low_resolution_outflow_refine_60s_0.csv' using 6:($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle\
-
-load 'common/velocity_wrapper.gnuplot'
-
-set obj 3 rect from 20.95,0 to 22,4.1
-set obj 3 fillstyle empty border -1 front lw 1
-
-load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_low_resolution_outflow_refine_60s_knudsen.gnuplot b/img/cylinder2d_low_resolution_outflow_refine_60s_knudsen.gnuplot
deleted file mode 100644
index ca0d5e9..0000000
--- a/img/cylinder2d_low_resolution_outflow_refine_60s_knudsen.gnuplot
+++ /dev/null
@@ -1,14 +0,0 @@
-plotname = "cylinder2d_low_resolution_outflow_refine_60s_knudsen"
-knudsen = 0.000866025
-
-load 'common/knudsen_fluid.gnuplot'
-
-plot 'data/cylinder2d_low_resolution_outflow_refine_60s_1.csv' using ($6+0.05):($7+0.05):(log($5/knudsen)/log(2)) palette pt 5 ps 5.3 notitle,\
-     'data/cylinder2d_low_resolution_outflow_refine_60s_0.csv' using 6:($7+0.05):(log($5/knudsen)/log(2)) palette pt 5 ps 2.6 notitle\
-
-load 'common/knudsen_wrapper.gnuplot'
-
-set obj 3 rect from 20.95,0 to 22,4.1
-set obj 3 fillstyle empty border -1 front lw 1
-
-load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.gnuplot b/img/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.gnuplot
new file mode 100644
index 0000000..5d5a46b
--- /dev/null
+++ b/img/cylinder2d_low_resolution_outflow_refine_n5_re100_16s.gnuplot
@@ -0,0 +1,19 @@
+plotname = "cylinder2d_low_resolution_outflow_refine_n5_re100_16s"
+
+load 'common/velocity_fluid.gnuplot'
+
+set yrange [0:4.2]
+
+plot 'data/cylinder2d_low_resolution_outflow_refine_n5_re100_16s_2.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 5.3 notitle,\
+     'data/cylinder2d_low_resolution_outflow_refine_n5_re100_16s_1.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle,\
+     'data/cylinder2d_low_resolution_outflow_refine_n5_re100_16s_0.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle\
+
+load 'common/velocity_wrapper.gnuplot'
+
+set obj 1 rect from 21.165,0 to 22,4.1
+set obj 1 fillstyle empty border -1 front lw 1
+
+set obj 2 rect from 21.65,0 to 22,4.1
+set obj 2 fillstyle empty border -1 front lw 1
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_optimized_low_resolution_grid_60s.gnuplot b/img/cylinder2d_optimized_low_resolution_grid_60s.gnuplot
deleted file mode 100644
index 7b9b453..0000000
--- a/img/cylinder2d_optimized_low_resolution_grid_60s.gnuplot
+++ /dev/null
@@ -1,27 +0,0 @@
-plotname = "cylinder2d_optimized_low_resolution_grid_60s"
-
-load 'common/velocity_fluid.gnuplot'
-
-plot 'data/cylinder2d_optimized_low_resolution_grid_60s_4.csv' using ($6+0.05):($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 5.3 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_3.csv' using ($6+0.05):($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_2.csv' using 6:($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_1.csv' using 6:($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 1.3 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_0.csv' using 6:($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.6 notitle,\
-
-load 'common/velocity_wrapper.gnuplot'
-
-set obj 1 rect from 0.8,0.2 to 7.3,3.9
-set obj 1 fillstyle empty border -1 front lw 1
-
-set obj 2 rect from 0.975,1.125 to 3.23,2.875
-set obj 2 fillstyle empty border -1 front lw 1
-
-set obj 3 rect from 1.295,1.345 to 2.675,2.7
-set obj 3 fillstyle empty border -1 front lw 1
-
-set obj 4 rect from 20.95,0 to 22,4.1
-set obj 4 fillstyle empty border -1 front lw 1
-
-set title "Geeignet dreifach verfeinertes Gitter mit 7329 Knoten"
-
-load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_optimized_low_resolution_grid_60s_knudsen.gnuplot b/img/cylinder2d_optimized_low_resolution_grid_60s_knudsen.gnuplot
deleted file mode 100644
index 301a4fb..0000000
--- a/img/cylinder2d_optimized_low_resolution_grid_60s_knudsen.gnuplot
+++ /dev/null
@@ -1,23 +0,0 @@
-plotname = "cylinder2d_optimized_low_resolution_grid_60s_knudsen"
-knudsen = 0.000866025
-
-load 'common/knudsen_fluid.gnuplot'
-
-plot 'data/cylinder2d_optimized_low_resolution_grid_60s_3.csv' using ($6+0.05):($7+0.05):(log($5/knudsen)/log(2)) palette pt 5 ps 5.3 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_2.csv' using 6:($7+0.05):(log($5/knudsen)/log(2)) palette pt 5 ps 2.6 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_1.csv' using 6:($7+0.05):(log($5/knudsen)/log(2)) palette pt 5 ps 2.6 notitle,\
-     'data/cylinder2d_optimized_low_resolution_grid_60s_0.csv' using 6:($7+0.05):(log($5/knudsen)/log(2)) palette pt 5 ps 1.6 notitle,\
-
-load 'common/knudsen_wrapper.gnuplot'
-
-set obj 1 rect from 0.75,0.2 to 8.85,3.9
-set obj 1 fillstyle empty border -1 front lw 1
-
-set obj 2 rect from 0.95,1.0 to 4.65,3.05
-set obj 2 fillstyle empty border -1 front lw 1
-set obj 2 fillstyle empty border -1 front lw 1
-
-set obj 3 rect from 20.95,0 to 22,4.1
-set obj 3 fillstyle empty border -1 front lw 1
-
-load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_optimized_refinement_n5_re100_16s.gnuplot b/img/cylinder2d_optimized_refinement_n5_re100_16s.gnuplot
new file mode 100644
index 0000000..8c206e9
--- /dev/null
+++ b/img/cylinder2d_optimized_refinement_n5_re100_16s.gnuplot
@@ -0,0 +1,33 @@
+plotname = "cylinder2d_optimized_refinement_n5_re100_16s"
+
+load 'common/velocity_fluid.gnuplot'
+
+set yrange [0:4.2]
+
+plot 'data/cylinder2d_optimized_refinement_n5_re100_16s_5.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 5.3 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_4.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_2.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.6 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_3.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 1.7 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_1.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 1.7 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_0.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.7 notitle\
+
+load 'common/velocity_wrapper.gnuplot'
+
+set obj 1 rect from 21.165,0 to 22,4.1
+set obj 1 fillstyle empty border -1 front lw 1
+
+set obj 2 rect from 21.65,0 to 22,4.1
+set obj 2 fillstyle empty border -1 front lw 1
+
+set obj 3 rect from 1.4,1.45 to 2.675,2.7
+set obj 3 fillstyle empty border -1 front lw 1
+
+set obj 4 rect from 0.97,0.355 to 6.05,3.75
+set obj 4 fillstyle empty border -1 front lw 1
+
+set obj 5 rect from 0.55,0.15 to 11.05,3.95
+set obj 5 fillstyle empty border -1 front lw 1
+
+set title "Geeignet dreifach verfeinertes Gitter mit 13454 Knoten"
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.gnuplot b/img/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.gnuplot
new file mode 100644
index 0000000..b31be02
--- /dev/null
+++ b/img/cylinder2d_optimized_refinement_n5_re100_16s_knudsen.gnuplot
@@ -0,0 +1,32 @@
+plotname = "cylinder2d_optimized_refinement_n5_re100_16s_knudsen"
+knudsen = 0.0011547
+
+load 'common/knudsen_fluid.gnuplot'
+
+set yrange [0:4.2]
+
+plot 'data/cylinder2d_optimized_refinement_n5_re100_16s_5.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 5.3 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_4.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 2.6 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_2.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 2.6 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_3.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 1.7 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_1.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 1.7 notitle,\
+     'data/cylinder2d_optimized_refinement_n5_re100_16s_0.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle\
+
+load 'common/knudsen_wrapper.gnuplot'
+
+set obj 1 rect from 21.165,0 to 22,4.1
+set obj 1 fillstyle empty border -1 front lw 1
+
+set obj 2 rect from 21.65,0 to 22,4.1
+set obj 2 fillstyle empty border -1 front lw 1
+
+set obj 3 rect from 1.4,1.45 to 2.675,2.7
+set obj 3 fillstyle empty border -1 front lw 1
+
+set obj 4 rect from 0.97,0.355 to 6.05,3.75
+set obj 4 fillstyle empty border -1 front lw 1
+
+set obj 5 rect from 0.55,0.15 to 11.05,3.95
+set obj 5 fillstyle empty border -1 front lw 1
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_single_refinement_n20_re100_16s.gnuplot b/img/cylinder2d_single_refinement_n20_re100_16s.gnuplot
new file mode 100644
index 0000000..39c2736
--- /dev/null
+++ b/img/cylinder2d_single_refinement_n20_re100_16s.gnuplot
@@ -0,0 +1,13 @@
+plotname = "cylinder2d_single_refinement_n20_re100_16s"
+
+load 'common/velocity_fluid.gnuplot'
+
+plot 'data/cylinder2d_single_refinement_n20_re100_16s_1.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 1.3 notitle,\
+     'data/cylinder2d_single_refinement_n20_re100_16s_0.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.7 notitle
+
+load 'common/velocity_wrapper.gnuplot'
+
+set obj 1 rect from 1.0,0.55 to 9,3.55
+set obj 1 fillstyle empty border -1 front lw 1
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_single_refinement_n20_re100_16s_knudsen.gnuplot b/img/cylinder2d_single_refinement_n20_re100_16s_knudsen.gnuplot
new file mode 100644
index 0000000..3b8197d
--- /dev/null
+++ b/img/cylinder2d_single_refinement_n20_re100_16s_knudsen.gnuplot
@@ -0,0 +1,14 @@
+plotname = "cylinder2d_single_refinement_n20_re100_16s_knudsen"
+knudsen = 0.000288675
+
+load 'common/knudsen_fluid.gnuplot'
+
+plot 'data/cylinder2d_single_refinement_n20_re100_16s_1.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 1.3 notitle,\
+'data/cylinder2d_single_refinement_n20_re100_16s_0.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle
+
+load 'common/knudsen_wrapper.gnuplot'
+
+set obj 1 rect from 1,0.55 to 9,3.55
+set obj 1 fillstyle empty border -1 front lw 1
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_unoptimized_low_resolution_grid_60s.gnuplot b/img/cylinder2d_unoptimized_low_resolution_grid_60s.gnuplot
deleted file mode 100644
index 80c3605..0000000
--- a/img/cylinder2d_unoptimized_low_resolution_grid_60s.gnuplot
+++ /dev/null
@@ -1,11 +0,0 @@
-plotname = "cylinder2d_unoptimized_low_resolution_grid_60s"
-
-load 'common/velocity_fluid.gnuplot'
-
-plot 'data/cylinder2d_unoptimized_low_resolution_grid_60s.csv' using ($6+0.05):($7+0.05):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.9 notitle,\
-
-load 'common/velocity_wrapper.gnuplot'
-
-set title "Uniform aufgelöstes Gitter mit 7326 Knoten"
-
-load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_unrefined_n12_re100_16s.gnuplot b/img/cylinder2d_unrefined_n12_re100_16s.gnuplot
new file mode 100644
index 0000000..81a0dfa
--- /dev/null
+++ b/img/cylinder2d_unrefined_n12_re100_16s.gnuplot
@@ -0,0 +1,11 @@
+plotname = "cylinder2d_unrefined_n12_re100_16s"
+
+load 'common/velocity_fluid.gnuplot'
+
+plot 'data/cylinder2d_unrefined_n12_re100_16s.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 2.25 notitle
+
+load 'common/velocity_wrapper.gnuplot'
+
+set title "Uniform aufgelöstes Gitter mit 13500 Knoten"
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_unrefined_n20_re100_16s.gnuplot b/img/cylinder2d_unrefined_n20_re100_16s.gnuplot
new file mode 100644
index 0000000..ab5c811
--- /dev/null
+++ b/img/cylinder2d_unrefined_n20_re100_16s.gnuplot
@@ -0,0 +1,9 @@
+plotname = "cylinder2d_unrefined_n20_re100_16s"
+
+load 'common/velocity_fluid.gnuplot'
+
+plot 'data/cylinder2d_unrefined_n20_re100_16s.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 1.3 notitle
+
+load 'common/velocity_wrapper.gnuplot'
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_unrefined_n20_re100_16s_knudsen.gnuplot b/img/cylinder2d_unrefined_n20_re100_16s_knudsen.gnuplot
new file mode 100644
index 0000000..56b9d6e
--- /dev/null
+++ b/img/cylinder2d_unrefined_n20_re100_16s_knudsen.gnuplot
@@ -0,0 +1,10 @@
+plotname = "cylinder2d_unrefined_n20_re100_16s_knudsen"
+knudsen = 0.000288675
+
+load 'common/knudsen_fluid.gnuplot'
+
+plot 'data/cylinder2d_unrefined_n20_re100_16s.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 1.3 notitle
+
+load 'common/knudsen_wrapper.gnuplot'
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_unrefined_n40_re100_16s.gnuplot b/img/cylinder2d_unrefined_n40_re100_16s.gnuplot
new file mode 100644
index 0000000..ccbd7ef
--- /dev/null
+++ b/img/cylinder2d_unrefined_n40_re100_16s.gnuplot
@@ -0,0 +1,12 @@
+plotname = "cylinder2d_unrefined_n40_re100_16s"
+
+load 'common/velocity_fluid.gnuplot'
+
+plot 'data/cylinder2d_unrefined_n40_re100_16s_0.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_unrefined_n40_re100_16s_1.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_unrefined_n40_re100_16s_2.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_unrefined_n40_re100_16s_3.csv' using ($6*10):($7*10):(sqrt($2*$2+$3*$3)) palette pt 5 ps 0.7 notitle
+
+load 'common/velocity_wrapper.gnuplot'
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/cylinder2d_unrefined_n40_re100_16s_knudsen.gnuplot b/img/cylinder2d_unrefined_n40_re100_16s_knudsen.gnuplot
new file mode 100644
index 0000000..81ac301
--- /dev/null
+++ b/img/cylinder2d_unrefined_n40_re100_16s_knudsen.gnuplot
@@ -0,0 +1,13 @@
+plotname = "cylinder2d_unrefined_n40_re100_16s_knudsen"
+knudsen = 0.000144338
+
+load 'common/knudsen_fluid.gnuplot'
+
+plot 'data/cylinder2d_unrefined_n40_re100_16s_0.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_unrefined_n40_re100_16s_1.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_unrefined_n40_re100_16s_2.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle,\
+     'data/cylinder2d_unrefined_n40_re100_16s_3.csv' using ($6*10):($7*10):(log($5/knudsen)/log(2)) palette pt 5 ps 0.7 notitle
+
+load 'common/knudsen_wrapper.gnuplot'
+
+load 'common/include_fluid.gnuplot'
diff --git a/img/data/cylinder2d_improved_grid_twice_refined_60s_0.csv b/img/data/cylinder2d_improved_grid_twice_refined_60s_0.csv
deleted file mode 100644
index c19ef54..0000000
--- a/img/data/cylinder2d_improved_grid_twice_refined_60s_0.csv
+++ /dev/null
@@ -1,46977 +0,0 @@
-geometry,ux,uy,p,knudsen,x,y,z
-1.00000000e+00,7.95862436e-01,-1.91651359e-01,9.91622508e-02,1.37314986e-04,1.00000000e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,7.98192799e-01,-1.94859296e-01,9.80397612e-02,1.38276228e-04,1.01250005e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,7.99988866e-01,-1.93943024e-01,1.01352505e-01,1.27060383e-04,1.00000000e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.02286208e-01,-1.97221965e-01,1.00240104e-01,1.28053944e-04,1.01250005e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.00595939e-01,-1.98080137e-01,9.68531147e-02,1.39458134e-04,1.02499998e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.04651916e-01,-2.00514734e-01,9.90506932e-02,1.29094900e-04,1.02499998e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.03069890e-01,-2.01314509e-01,9.56015810e-02,1.40876306e-04,1.03750002e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.07099283e-01,-2.03826293e-01,9.77956578e-02,1.30276079e-04,1.03750002e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.05620611e-01,-2.04560548e-01,9.42873508e-02,1.42484088e-04,1.04999995e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.09619248e-01,-2.07150102e-01,9.64774117e-02,1.31859779e-04,1.04999995e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.08254361e-01,-2.07817256e-01,9.29143503e-02,1.44208636e-04,1.06250000e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.12225401e-01,-2.10488111e-01,9.50915590e-02,1.33398033e-04,1.06250000e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.10969114e-01,-2.11082563e-01,9.14765745e-02,1.46143866e-04,1.07500005e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.14908743e-01,-2.13834032e-01,9.36454609e-02,1.35369060e-04,1.07500005e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.13763440e-01,-2.14354813e-01,8.99692997e-02,1.48387699e-04,1.08749998e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.17680717e-01,-2.17190698e-01,9.21226740e-02,1.37357099e-04,1.08749998e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.16641748e-01,-2.17631683e-01,8.83926302e-02,1.50855514e-04,1.10000002e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.20533812e-01,-2.20551893e-01,9.05310288e-02,1.39830139e-04,1.10000002e+00,1.01250005e+00,0.00000000e+00
-1.00000000e+00,8.19608212e-01,-2.20910996e-01,8.67463350e-02,1.53462373e-04,1.11249995e+00,1.00000000e+00,0.00000000e+00
-1.00000000e+00,8.23479354e-01,-2.23919302e-01,8.88621062e-02,1.42246558e-04,1.11249995e+00,1.01250005e+00,0.00000000e+00
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