1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
|
#----------------------------------------------------------------------------
# $Id: x22.tcl,v 1.1 2004/05/21 15:09:27 andrewross Exp $
#----------------------------------------------------------------------------
# Vector plot demo.
proc x22 {{w loopback}} {
matrix arrow_x f 6 = {-0.5, 0.5, 0.3, 0.5, 0.3, 0.5}
matrix arrow_y f 6 = {0.0, 0.0, 0.2, 0.0, -0.2, 0.0}
matrix arrow2_x f 6 = {-0.5, 0.3, 0.3, 0.5, 0.3, 0.3}
matrix arrow2_y f 6 = {0.0, 0.0, 0.2, 0.0, -0.2, 0.0}
circulation $w
set narr 6
set fill 0
$w cmd plsvect arrow_x arrow_y $narr $fill
constriction $w
set fill 1
$w cmd plsvect arrow2_x arrow2_y $narr $fill
constriction $w
potential $w
}
# Vector plot of circulation about the origin
proc circulation {w} {
set nx 20
set ny 20
set dx 1.0
set dy 1.0
set xmin [expr (-$nx/2*$dx)]
set xmax [expr ($nx/2*$dx)]
set ymin [expr (-$ny/2*$dy)]
set ymax [expr ($ny/2*$dy)]
matrix xg f $nx $ny
matrix yg f $nx $ny
matrix u f $nx $ny
matrix v f $nx $ny
# Create data - circulation around the origin.
for {set i 0} {$i < $nx} {incr i} {
set x [expr (($i-$nx/2+0.5)*$dx) ]
for {set j 0} {$j < $ny} {incr j} {
set y [expr (($j-$ny/2+0.5)*$dy)]
xg $i $j = $x
yg $i $j = $y
u $i $j = $y
v $i $j = [expr (-1.0*$x)]
}
}
# Plot vectors with default arrows
$w cmd plenv $xmin $xmax $ymin $ymax 0 0
$w cmd pllab "(x)" "(y)" "#frPLplot Example 22 - circulation"
$w cmd plcol0 2
$w cmd plvect u v 0.0 "pltr2" xg yg
$w cmd plcol0 1
}
# Vector plot of flow through a constricted pipe
proc constriction {w} {
set pi 3.14159265358979323846
set nx 20
set ny 20
set dx 1.0
set dy 1.0
set xmin [expr (-$nx/2*$dx)]
set xmax [expr ($nx/2*$dx)]
set ymin [expr (-$ny/2*$dy)]
set ymax [expr ($ny/2*$dy)]
matrix xg f $nx $ny
matrix yg f $nx $ny
matrix u f $nx $ny
matrix v f $nx $ny
set Q 2.0
# Create data - circulation around the origin.
for {set i 0} {$i < $nx} {incr i} {
set x [expr (($i-$nx/2+0.5)*$dx) ]
for {set j 0} {$j < $ny} {incr j} {
set y [expr (($j-$ny/2+0.5)*$dy)]
xg $i $j = $x
yg $i $j = $y
set b [expr ($ymax/4.0*(3.0-cos($pi*$x/$xmax)))]
if {abs($y) < $b} {
set dbdx [expr ($ymax/4.0*sin($pi*$x/$xmax)*$y/$b)]
u $i $j = [expr ($Q*$ymax/$b)]
v $i $j = [expr ($Q*$ymax/$b*$dbdx)]
} else {
u $i $j = 0.0
v $i $j = 0.0
}
}
}
# Plot vectors with default arrows
$w cmd plenv $xmin $xmax $ymin $ymax 0 0
$w cmd pllab "(x)" "(y)" "#frPLplot Example 22 - constriction"
$w cmd plcol0 2
$w cmd plvect u v -0.5 "pltr2" xg yg
$w cmd plcol0 1
}
# Vector plot of the gradient of a shielded potential (see example 9)
proc potential {w} {
set pi 3.14159265358979323846
set nr 20
set ntheta 20
set nper 100
set nlevel 10
matrix xg f $nr $ntheta
matrix yg f $nr $ntheta
matrix u f $nr $ntheta
matrix v f $nr $ntheta
matrix z f $nr $ntheta
# Potential inside a conducting cylinder (or sphere) by method of images.
# Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
# Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
# Also put in smoothing term at small distances.
set rmax $nr
set eps [expr 2.]
set q1 [expr 1.]
set d1 [expr $rmax/4.]
set q1i [expr - $q1*$rmax/$d1]
set d1i [expr pow($rmax,2)/$d1]
set q2 [expr -1.]
set d2 [expr $rmax/4.]
set q2i [expr - $q2*$rmax/$d2]
set d2i [expr pow($rmax,2)/$d2]
for {set i 0} {$i < $nr} {incr i} {
set r [expr 0.5 + $i]
for {set j 0} {$j < $ntheta} {incr j} {
set theta [expr {(2. * $pi / ($ntheta - 1.))*(0.5 + $j)}]
set x [expr {$r * cos($theta)}]
set y [expr {$r * sin($theta)}]
xg $i $j = $x
yg $i $j = $y
set div1 [expr {sqrt(pow($x-$d1,2) + pow($y-$d1,2) +
pow($eps,2))}]
set div1i [expr {sqrt(pow($x-$d1i,2) + pow($y-$d1i,2) + pow($eps,2))}]
set div2 [expr {sqrt(pow($x-$d2,2) + pow($y+$d2,2) +
pow($eps,2))}]
set div2i [expr {sqrt(pow($x-$d2i,2) + pow($y+$d2i,2) + pow($eps,2))}]
z $i $j = [expr {$q1/$div1 + $q1i/$div1i + $q2/$div2 + $q2i/$div2i}]
u $i $j = [expr {-$q1*($x-$d1)/pow($div1,3) - $q1i*($x-$d1i)/pow($div1i,3) -
$q2*($x-$d2)/pow($div2,3) - $q2i*($x-$d2i)/pow($div2i,3)}]
v $i $j = [expr {-$q1*($y-$d1)/pow($div1,3) - $q1i*($y-$d1i)/pow($div1i,3) -
$q2*($y+$d2)/pow($div2,3) - $q2i*($y+$d2i)/pow($div2i,3)}]
}
}
set xmin [xg 0 0]
set xmax $xmin
set ymin [yg 0 0]
set ymax $ymin
set zmin [z 0 0]
set zmax $zmin
for {set i 0} {$i < $nr} {incr i} {
for {set j 0} {$j < $ntheta} {incr j} {
if {[xg $i $j] < $xmin} { set xmin [xg $i $j] }
if {[xg $i $j] > $xmax} { set xmax [xg $i $j] }
if {[yg $i $j] < $ymin} { set ymin [yg $i $j] }
if {[yg $i $j] > $ymax} { set ymax [yg $i $j] }
if {[z $i $j] < $zmin} { set zmin [z $i $j] }
if {[z $i $j] > $zmax} { set zmax [z $i $j] }
}
}
$w cmd plenv $xmin $xmax $ymin $ymax 0 0
$w cmd pllab "(x)" "(y)" "#frPLplot Example 22 - potential gradient vector plot"
# Plot contours of the potential
set dz [expr (($zmax-$zmin)/$nlevel)]
matrix clevel f $nlevel
for {set i 0} {$i < $nlevel} {incr i} {
clevel $i = [expr {$zmin + ($i + 0.5)*$dz}]
}
$w cmd plcol0 3
$w cmd pllsty 2
$w cmd plcont z clevel "pltr2" xg yg
$w cmd pllsty 1
$w cmd plcol0 1
# Plot vectors with default arrows
$w cmd plcol0 2
$w cmd plvect u v 25.0 "pltr2" xg yg
$w cmd plcol0 1
# Plot the perimeter of the cylinder
matrix px f $nper
matrix py f $nper
set dtheta [expr (2.0*$pi/($nper-1.0))]
for {set i 0} {$i < $nper} {incr i} {
set theta [expr $dtheta*$i]
px $i = [expr ($rmax*cos($theta))]
py $i = [expr ($rmax*sin($theta))]
}
$w cmd plline $nper px py
}
|
