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
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
|
import pyopencl as cl
mf = cl.mem_flags
from string import Template
import numpy
import time
import matplotlib
import matplotlib.pyplot as plt
matplotlib.use('AGG')
kernel = """
unsigned int indexOfDirection(int i, int j) {
return (i+1) + 3*(1-j);
}
unsigned int indexOfCell(int x, int y)
{
return y * $nX + x;
}
unsigned int idx(int x, int y, int i, int j) {
return indexOfDirection(i,j)*$nCells + indexOfCell(x,y);
}
__global float f_i(__global __read_only float* f, int x, int y, int i, int j) {
return f[idx(x,y,i,j)];
}
__kernel void collide_and_stream(__global __write_only float* f_a,
__global __read_only float* f_b,
__global __read_only 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;
}
const float f_curr_0 = f_i(f_b, cell.x+1, cell.y-1, -1, 1);
const float f_curr_1 = f_i(f_b, cell.x , cell.y-1, 0, 1);
const float f_curr_2 = f_i(f_b, cell.x-1, cell.y-1, 1, 1);
const float f_curr_3 = f_i(f_b, cell.x+1, cell.y , -1, 0);
const float f_curr_4 = f_i(f_b, cell.x , cell.y , 0, 0);
const float f_curr_5 = f_i(f_b, cell.x-1, cell.y , 1, 0);
const float f_curr_6 = f_i(f_b, cell.x+1, cell.y+1, -1,-1);
const float f_curr_7 = f_i(f_b, cell.x , cell.y+1, 0,-1);
const float f_curr_8 = f_i(f_b, cell.x-1, cell.y+1, 1,-1);
const float ux0 = f_curr_3 + f_curr_6;
const float ux1 = f_curr_1 + f_curr_2;
const float ux2 = 1.0/(f_curr_0 + f_curr_4 + f_curr_5 + f_curr_7 + f_curr_8 + ux0 + ux1);
const float ux3 = f_curr_0 - f_curr_8;
float u_x = -ux2*(-f_curr_2 - f_curr_5 + ux0 + ux3);
float u_y = ux2*(-f_curr_6 - f_curr_7 + ux1 + ux3);
if ( m == 2 ) {
u_x = 0.0;
u_y = 0.0;
}
const float x0 = f_curr_0 + f_curr_1 + f_curr_2 + f_curr_3 + f_curr_4 + f_curr_5 + f_curr_6 + f_curr_7 + f_curr_8;
const float x1 = 6*u_y;
const float x2 = 6*u_x;
const float x3 = pow(u_y, 2);
const float x4 = 3*x3;
const float x5 = pow(u_x, 2);
const float x6 = 3*x5;
const float x7 = x6 - 2;
const float x8 = x4 + x7;
const float x9 = x2 + x8;
const float x10 = 1.0/$tau;
const float x11 = (1.0/72.0)*x10;
const float x12 = 6*x3;
const float x13 = x1 - x6 + 2;
const float x14 = (1.0/18.0)*x10;
const float x15 = -x4;
const float x16 = 9*pow(u_x + u_y, 2);
const float x17 = -x2;
const float x18 = x15 + 6*x5 + 2;
f_a[0*$nCells + gid] = f_curr_0 - x11*(72*f_curr_0 + x0*(-x1 + x9 - 9*pow(-u_x + u_y, 2)));
f_a[1*$nCells + gid] = f_curr_1 - x14*(18*f_curr_1 - x0*(x12 + x13));
f_a[2*$nCells + gid] = f_curr_2 - x11*(72*f_curr_2 - x0*(x13 + x15 + x16 + x2));
f_a[3*$nCells + gid] = f_curr_3 - x14*(18*f_curr_3 - x0*(x17 + x18));
f_a[4*$nCells + gid] = f_curr_4 - 1.0/9.0*x10*(9*f_curr_4 + 2*x0*x8);
f_a[5*$nCells + gid] = f_curr_5 - x14*(18*f_curr_5 - x0*(x18 + x2));
f_a[6*$nCells + gid] = f_curr_6 - x11*(72*f_curr_6 + x0*(x1 - x16 + x9));
f_a[7*$nCells + gid] = f_curr_7 - x14*(18*f_curr_7 + x0*(x1 - x12 + x7));
f_a[8*$nCells + gid] = f_curr_8 - x11*(72*f_curr_8 + x0*(x1 + x17 + x8 - 9*pow(u_x - u_y, 2)));
}
__kernel void collect_moments(__global __read_only float* f,
__global __write_only float* moments)
{
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 float f_curr_0 = f[0*$nCells + gid];
const float f_curr_1 = f[1*$nCells + gid];
const float f_curr_2 = f[2*$nCells + gid];
const float f_curr_3 = f[3*$nCells + gid];
const float f_curr_4 = f[4*$nCells + gid];
const float f_curr_5 = f[5*$nCells + gid];
const float f_curr_6 = f[6*$nCells + gid];
const float f_curr_7 = f[7*$nCells + gid];
const float f_curr_8 = f[8*$nCells + gid];
const float ux0 = f_curr_3 + f_curr_6;
const float ux1 = f_curr_1 + f_curr_2;
const float ux2 = 1.0/(f_curr_0 + f_curr_4 + f_curr_5 + f_curr_7 + f_curr_8 + ux0 + ux1);
const float ux3 = f_curr_0 - f_curr_8;
moments[0*$nCells + gid] = f_curr_0 + ux1 + ux0 + f_curr_4 + f_curr_5 + f_curr_7 + f_curr_8;
moments[1*$nCells + gid] = -ux2*(-f_curr_2 - f_curr_5 + ux0 + ux3);
moments[2*$nCells + gid] = ux2*(-f_curr_6 - f_curr_7 + ux1 + ux3);
}"""
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.np_stat_moments = []
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)] = 2
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,
'nCells': self.nCells,
'tau': '0.8f'
})).build() #'-cl-single-precision-constant -cl-fast-relaxed-math')
def collect_moments(self):
if self.tick:
self.program.collect_moments(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_b, self.cl_moments)
else:
self.program.collect_moments(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_a, self.cl_moments)
cl.enqueue_copy(LBM.queue, self.np_moments, LBM.cl_moments).wait();
self.np_stat_moments.append(self.np_moments.copy())
def evolve(self):
if self.tick:
self.tick = False
self.program.collide_and_stream(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_a, self.cl_pop_b, self.cl_material)
else:
self.tick = True
self.program.collide_and_stream(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_b, self.cl_pop_a, self.cl_material)
def sync(self):
self.queue.finish()
def generate_moment_plots(self):
for i, np_moments in enumerate(self.np_stat_moments):
print("Generating plot %d of %d." % (i+1, len(self.np_stat_moments)))
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[y-1,x-1] = np_moments[0,self.idx(x,y)]
plt.figure(figsize=(10, 10))
plt.imshow(density, vmin=0.2, vmax=2.0, cmap=plt.get_cmap("seismic"))
plt.savefig("result/density_" + str(i) + ".png", bbox_inches='tight', pad_inches=0)
self.np_stat_moments = []
def MLUPS(cells, steps, time):
return cells * steps / time * 1e-6
nUpdates = 1000
nStat = 100
print("Initializing simulation...\n")
LBM = D2Q9_BGK_Lattice(1024, 1024)
print("Starting simulation using %d cells...\n" % LBM.nCells)
lastStat = time.time()
for i in range(1,nUpdates+1):
LBM.evolve()
if i % nStat == 0:
LBM.sync()
print("i = %4d; %3.0f MLUPS" % (i, MLUPS(LBM.nCells, nStat, time.time() - lastStat)))
LBM.collect_moments()
lastStat = time.time()
print("\nConcluded simulation.\n")
LBM.generate_moment_plots()
|
