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import pyopencl as cl
mf = cl.mem_flags
from string import Template
import numpy
import matplotlib.pyplot as plt
import time
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 __write_only float* moments,
__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)));
moments[gid] = x0;
}"""
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)] = 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 evolve(self):
if self.tick:
self.tick = False
self.program.collide_and_stream(self.queue, (self.nX,self.nY), (64,1), self.cl_pop_a, self.cl_pop_b, self.cl_moments, self.cl_material)
else:
self.tick = True
self.program.collide_and_stream(self.queue, (self.nX,self.nY), (64,1), self.cl_pop_b, self.cl_pop_a, self.cl_moments, self.cl_material)
def sync(self):
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[y-1,x-1] = self.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)
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):
if i % nStat == 0:
LBM.sync()
#LBM.show(i)
print("i = %4d; %3.0f MLUPS" % (i, MLUPS(LBM.nCells, nStat, time.time() - lastStat)))
lastStat = time.time()
LBM.evolve()
LBM.show(nUpdates)
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