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
225
226
|
import pyopencl as cl
mf = cl.mem_flags
from string import Template
import numpy
import matplotlib.pyplot as plt
from timeit import default_timer as timer
kernel = """
float constant w[9] = {
1./36., 1./9., 1./36.,
1./9. , 4./9., 1./9. ,
1./36 , 1./9., 1./36.
};
unsigned int indexOfDirection(int i, int j) {
return (i+1) + 3*(1-j);
}
unsigned int indexOfCell(int x, int y)
{
return y * $nX + x;
}
unsigned int idx(int x, int y, int i, int j) {
return indexOfDirection(i,j)*$nX*$nY + indexOfCell(x,y);
}
__global float f_i(__global const float* f, int x, int y, int i, int j) {
return f[idx(x,y,i,j)];
}
float comp(int i, int j, float2 v) {
return i*v.x + j*v.y;
}
float sq(float x) {
return x*x;
}
float f_eq(float w, float d, float2 v, int i, int j, float dotv) {
return w * d * (1 + 3*comp(i,j,v) + 4.5*sq(comp(i,j,v)) - 1.5*dotv);
}
__kernel void collide_and_stream(__global float* f_a,
__global const float* f_b,
__global float* moments,
__global const int* material)
{
const unsigned int gid = indexOfCell(get_global_id(0), get_global_id(1));
const uint2 cell = (uint2)(get_global_id(0), get_global_id(1));
const int m = material[gid];
if ( m == 0 ) {
return;
}
float f0 = f_b[0*$nX*$nY + gid];
float d = f0;
float f1 = f_b[1*$nX*$nY + gid];
d += f1;
float f2 = f_b[2*$nX*$nY + gid];
d += f2;
float f3 = f_b[3*$nX*$nY + gid];
d += f3;
float f4 = f_b[4*$nX*$nY + gid];
d += f4;
float f5 = f_b[5*$nX*$nY + gid];
d += f5;
float f6 = f_b[6*$nX*$nY + gid];
d += f6;
float f7 = f_b[7*$nX*$nY + gid];
d += f7;
float f8 = f_b[8*$nX*$nY + gid];
d += f8;
const float2 v = (float2)(
(f5 - f3 + f2 - f6 + f8 - f0) / d,
(f1 - f7 + f2 - f6 - f8 + f0) / d
);
const float dotv = dot(v,v);
f0 = (1.0 - $tau) * (f_i(f_b, cell.x+1, cell.y-1, -1, 1)) + $tau * f_eq(w[0], d,v,-1, 1, dotv);
f1 = (1.0 - $tau) * (f_i(f_b, cell.x , cell.y-1, 0, 1)) + $tau * f_eq(w[1], d,v, 0, 1, dotv);
f2 = (1.0 - $tau) * (f_i(f_b, cell.x-1, cell.y-1, 1, 1)) + $tau * f_eq(w[2], d,v, 1, 1, dotv);
f3 = (1.0 - $tau) * (f_i(f_b, cell.x+1, cell.y , -1, 0)) + $tau * f_eq(w[3], d,v,-1, 0, dotv);
f4 = (1.0 - $tau) * (f_i(f_b, cell.x , cell.y , 0, 0)) + $tau * f_eq(w[4], d,v, 0, 0, dotv);
f5 = (1.0 - $tau) * (f_i(f_b, cell.x-1, cell.y , 1, 0)) + $tau * f_eq(w[5], d,v, 1, 0, dotv);
f6 = (1.0 - $tau) * (f_i(f_b, cell.x+1, cell.y+1, -1,-1)) + $tau * f_eq(w[6], d,v,-1,-1, dotv);
f7 = (1.0 - $tau) * (f_i(f_b, cell.x , cell.y+1, 0,-1)) + $tau * f_eq(w[7], d,v, 0,-1, dotv);
f8 = (1.0 - $tau) * (f_i(f_b, cell.x-1, cell.y+1, 1,-1)) + $tau * f_eq(w[8], d,v, 1,-1, dotv);
f_a[0*$nX*$nY + gid] = f0;
f_a[1*$nX*$nY + gid] = f1;
f_a[2*$nX*$nY + gid] = f2;
f_a[3*$nX*$nY + gid] = f3;
f_a[4*$nX*$nY + gid] = f4;
f_a[5*$nX*$nY + gid] = f5;
f_a[6*$nX*$nY + gid] = f6;
f_a[7*$nX*$nY + gid] = f7;
f_a[8*$nX*$nY + gid] = f8;
moments[1*gid] = d;
moments[2*gid] = v.x;
moments[3*gid] = v.y;
}"""
class D2Q9_BGK_Lattice:
def idx(self, x, y):
return y * self.nX + x;
def __init__(self, nX, nY):
self.nX = nX
self.nY = nY
self.nCells = nX * nY
self.tick = True
self.platform = cl.get_platforms()[0]
self.context = cl.Context(properties=[(cl.context_properties.PLATFORM, self.platform)])
self.queue = cl.CommandQueue(self.context)
self.np_pop_a = numpy.ndarray(shape=(9, self.nCells), dtype=numpy.float32)
self.np_pop_b = numpy.ndarray(shape=(9, self.nCells), dtype=numpy.float32)
self.np_moments = numpy.ndarray(shape=(3, self.nCells), dtype=numpy.float32)
self.np_material = numpy.ndarray(shape=(self.nCells, 1), dtype=numpy.int32)
self.setup_geometry()
self.equilibrilize()
self.setup_anomaly()
self.cl_pop_a = cl.Buffer(self.context, mf.READ_WRITE | mf.USE_HOST_PTR, hostbuf=self.np_pop_a)
self.cl_pop_b = cl.Buffer(self.context, mf.READ_WRITE | mf.USE_HOST_PTR, hostbuf=self.np_pop_b)
self.cl_material = cl.Buffer(self.context, mf.READ_ONLY | mf.USE_HOST_PTR, hostbuf=self.np_material)
self.cl_moments = cl.Buffer(self.context, mf.READ_WRITE | mf.USE_HOST_PTR, hostbuf=self.np_moments)
self.build_kernel()
def setup_geometry(self):
self.np_material[:] = 0
for x in range(1,self.nX-1):
for y in range(1,self.nY-1):
if x == 1 or y == 1 or x == self.nX-2 or y == self.nY-2:
self.np_material[self.idx(x,y)] = -1
else:
self.np_material[self.idx(x,y)] = 1
def equilibrilize(self):
self.np_pop_a[(0,2,6,8),:] = 1./36.
self.np_pop_a[(1,3,5,7),:] = 1./9.
self.np_pop_a[4,:] = 4./9.
self.np_pop_b[(0,2,6,8),:] = 1./36.
self.np_pop_b[(1,3,5,7),:] = 1./9.
self.np_pop_b[4,:] = 4./9.
def setup_anomaly(self):
bubbles = [ [ self.nX//4, self.nY//4],
[ self.nX//4,self.nY-self.nY//4],
[self.nX-self.nX//4, self.nY//4],
[self.nX-self.nX//4,self.nY-self.nY//4] ]
for x in range(0,self.nX-1):
for y in range(0,self.nY-1):
for [a,b] in bubbles:
if numpy.sqrt((x-a)*(x-a)+(y-b)*(y-b)) < self.nX//10:
self.np_pop_a[:,self.idx(x,y)] = 1./24.
self.np_pop_b[:,self.idx(x,y)] = 1./24.
def build_kernel(self):
self.program = cl.Program(self.context, Template(kernel).substitute({
'nX' : self.nX,
'nY' : self.nY,
'tau': 0.56
})).build()
def evolve(self):
if self.tick:
self.tick = False
self.program.collide_and_stream(self.queue, (self.nX,self.nY), (256,1), self.cl_pop_a, self.cl_pop_b, self.cl_moments, self.cl_material)
self.queue.finish()
else:
self.tick = True
self.program.collide_and_stream(self.queue, (self.nX,self.nY), (256,1), self.cl_pop_b, self.cl_pop_a, self.cl_moments, self.cl_material)
self.queue.finish()
def show(self, i):
cl.enqueue_copy(LBM.queue, LBM.np_moments, LBM.cl_moments).wait();
density = numpy.ndarray(shape=(self.nX-2, self.nY-2))
for y in range(1,self.nY-1):
for x in range(1,self.nX-1):
density[x-1,y-1] = self.np_moments[0,self.idx(x,y)]
plt.imshow(density, vmin=0.2, vmax=2.0, cmap=plt.get_cmap("seismic"))
plt.savefig("result/density_" + str(i) + ".png")
def MLUPS(cells, steps, time):
return ((cells*steps) / time) / 1000000
LBM = D2Q9_BGK_Lattice(1024, 1024)
nUpdates = 1000
start = timer()
for i in range(0,nUpdates):
LBM.evolve()
end = timer()
runtime = end - start
print("Cells: " + str(LBM.nCells))
print("Updates: " + str(nUpdates))
print("Time: " + str(runtime))
print("MLUPS: " + str(MLUPS(LBM.nCells, nUpdates, end - start)))
LBM.show(nUpdates)
|
