commit 31c2212c8ce359ecafdd1c9dae46416d94847632
parent a40c8e83f2016532e87b22f58496e6e2a5176e17
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Sun, 15 Mar 2020 10:46:56 +0300
Update plots.
Diffstat:
5 files changed, 49 insertions(+), 14 deletions(-)
diff --git a/Makefile b/Makefile
@@ -44,5 +44,7 @@ build:
clean:
@rm -rf build
-.PHONY: build clean
+diff:
+ @python3 python/wind-diff.py
+.PHONY: build clean diff
diff --git a/gnuplot/velocity.gnuplot b/gnuplot/velocity.gnuplot
@@ -7,15 +7,15 @@ static_roll = 0.246736
unset key
set grid
set border 1+2 back
-set xtics nomirror out
-set ytics nomirror out
+set xtics nomirror out offset 0,0.5
+set ytics nomirror out offset 0.5,0
set xrange [0:*]
set yrange [0:*]
load 'gnuplot/rdbu.pal'
set multiplot layout 1,2
-set xlabel 'Wind velocity, m/s'
+set xlabel 'Wind velocity, m/s' offset 0,1
set ylabel 'Roll angle, °' offset 1.5,0
plot 'gnuplot/roll' using 1:(($2-static_roll)*s) with lines smooth csplines ls 1 lw 2
diff --git a/gnuplot/verification.gnuplot b/gnuplot/verification.gnuplot
@@ -2,8 +2,8 @@ set terminal svg dynamic size 1080/4*1.9, 1080/4 round enhanced font 'Liberation
set output "build/gnuplot/verification.svg"
#set key outside top center
unset key
-set xtics -50,25,50 out nomirror
-set ytics -50,25,50 out nomirror
+set xtics -50,25,50 out nomirror offset 0,0.5
+set ytics -50,25,50 out nomirror offset 0.5,0
set xrange [-52:52]
set yrange [-52:52]
set border 1+2
@@ -11,6 +11,8 @@ set size square
set size ratio -1
load 'gnuplot/rdbu.pal'
set cbrange [0:100]
+set xlabel 'x' offset 0,1
+set ylabel 'y' offset 1,0
s = 0.05
set multiplot layout 1,2
set object 1 circle front at 0,0 size 54.8858/2 fillcolor rgb "black" lw 0.5
diff --git a/main.tex b/main.tex
@@ -302,14 +302,9 @@ vector in cartesian coordinates). Then the solution is written as
and reduces to general form of the solution for potential flow around a
cylinder given in~\eqref{eq-solution-cylinder}.
-In order to be compatible with the surface of any object, solution near the
-boundary \eqref{eq-solution-near-the-boundary} uses different term \(s\) than
-the solution for potential flow around a cylinder which makes reflected
-velocity term reach maximum value for the point on the boundary, and for the
-point near the boundary the solution includes reflected velocity vectors for
-each panel. We compared both solutions (see fig.~\ref{fig-verification}) for a
-cylinder with \(R=27.4429\), and discovered that maximum root square error
-between the two is less than 1\%.
+We compared both solutions (see fig.~\ref{fig-verification}) for a cylinder
+with \(R=27.4429\), and discovered that maximum distance between velocity
+fields produced from both of them is 11\%.
\begin{figure}
\centering
@@ -372,6 +367,13 @@ opposite directions and cancel each other out. At top-most and bottom-most point
incident and reflected particle velocities have the same direction and
total velocity is two times larger than the velocity of the flow.
+In order to be compatible with the surface of any object, solution near the
+boundary \eqref{eq-solution-near-the-boundary} uses different term \(s\) than
+the solution for potential flow around a cylinder which makes reflected
+velocity term reach maximum value for the point on the boundary, and for the
+point near the boundary the solution includes reflected velocity vectors for
+each panel.
+
\section{Conclusion}
diff --git a/python/wind-diff.py b/python/wind-diff.py
@@ -0,0 +1,29 @@
+import math
+
+def read_last_column(filename):
+ result = []
+ with open(filename) as f1:
+ result = [[float(p[0]),float(p[1])] for p in
+ [line.split()[2:4] for line in f1.readlines()]]
+ return result
+
+def length(v):
+ return math.sqrt(v[0]*v[0]+v[1]*v[1])
+
+w1 = read_last_column('gnuplot/wind.orig')
+w2 = read_last_column('gnuplot/wind.our')
+
+diff_max = 0
+length_max = 0
+for wind_orig, wind_our in zip(w1,w2):
+ len1 = length(wind_orig)
+ len2 = length(wind_our)
+ #diff = (abs(100-(len2 / len1 * 100)))
+ diff = abs(len2 - len1)
+ if (len1 > length_max): length_max = len1
+ if (len2 > length_max): length_max = len2
+ if (diff > diff_max): diff_max = diff
+
+print('Max. velocity: {}'.format(length_max))
+print('Max. difference: {}'.format(diff_max))
+print('Max. error: {}'.format(diff_max/length_max*100))
