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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);
}
uint2 cellAtIndex(unsigned int gid)
{
const int y = gid / $nX;
return (uint2)(gid - $nX*y, y);
}
__global float* f_i(__global float* f, int x, int y, int i, int j) {
return f + idx(x,y,i,j);
}
float comp(int i, int j, float2 v) {
return i*v.x + j*v.y;
}
float sq(float x) {
return x*x;
}
float density(__global const float* f, unsigned int gid) {
return f[0*$nX*$nY + gid]
+ f[1*$nX*$nY + gid]
+ f[2*$nX*$nY + gid]
+ f[3*$nX*$nY + gid]
+ f[4*$nX*$nY + gid]
+ f[5*$nX*$nY + gid]
+ f[6*$nX*$nY + gid]
+ f[7*$nX*$nY + gid]
+ f[8*$nX*$nY + gid];
}
float2 velocity(__global const float* f, float d, unsigned int gid)
{
return (float2)(
(f[5*$nX*$nY+gid] - f[3*$nX*$nY+gid] + f[2*$nX*$nY+gid] - f[6*$nX*$nY+gid] + f[8*$nX*$nY+gid] - f[0*$nX*$nY+gid]) / d,
(f[1*$nX*$nY+gid] - f[7*$nX*$nY+gid] + f[2*$nX*$nY+gid] - f[6*$nX*$nY+gid] - f[8*$nX*$nY+gid] + f[0*$nX*$nY+gid]) / d
);
}
float f_eq(float d, float2 v, int i, int j) {
return w[indexOfDirection(i,j)] * d * (1 + 3*comp(i,j,v) + 4.5*sq(comp(i,j,v)) - 1.5*dot(v,v));
}
__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;
}
const float d = density(f_b, gid);
const float2 v = velocity(f_b, d, gid);
for ( int i = -1; i <= 1; ++i ) {
for ( int j = 1; j >= -1; --j ) {
*f_i(f_a, cell.x, cell.y, m*i, m*j) = *f_i(f_b, cell.x-i, cell.y-j, i, j)
+ $tau * (f_eq(d,v,i,j) - *f_i(f_b, cell.x-i, cell.y-j, i, j));
}
}
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), (16,64), 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), (16,64), 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)
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