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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 = """
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 * $nX + x;
}
unsigned int idx(int x, int y, int i, int j) {
return indexOfDirection(i,j)*$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)];
}
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.f + 3.f*comp(i,j,v) + 4.5f*sq(comp(i,j,v)) - 1.5f*dotv);
}
__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;
}
float f0 = f_i(f_b, cell.x+1, cell.y-1, -1, 1);
float f1 = f_i(f_b, cell.x , cell.y-1, 0, 1);
float f2 = f_i(f_b, cell.x-1, cell.y-1, 1, 1);
float f3 = f_i(f_b, cell.x+1, cell.y , -1, 0);
float f4 = f_i(f_b, cell.x , cell.y , 0, 0);
float f5 = f_i(f_b, cell.x-1, cell.y , 1, 0);
float f6 = f_i(f_b, cell.x+1, cell.y+1, -1,-1);
float f7 = f_i(f_b, cell.x , cell.y+1, 0,-1);
float f8 = f_i(f_b, cell.x-1, cell.y+1, 1,-1);
const float d = f0 + f1 + f2 + f3 + f4 + f5 + f6 + f7 + f8;
float2 v = (float2)(
(f5 - f3 + f2 - f6 + f8 - f0) / d,
(f1 - f7 + f2 - f6 - f8 + f0) / d
);
if ( m == 2 ) {
v = (float2)(0.0f, 0.0f);
}
if ( m == 3 ) {
v = (float2)(0.1f, 0.0f);
}
const float dotv = dot(v,v);
f0 += $omega * (f_eq(w[0], d,v,-1, 1, dotv) - f0);
f1 += $omega * (f_eq(w[1], d,v, 0, 1, dotv) - f1);
f2 += $omega * (f_eq(w[2], d,v, 1, 1, dotv) - f2);
f3 += $omega * (f_eq(w[3], d,v,-1, 0, dotv) - f3);
f4 += $omega * (f_eq(w[4], d,v, 0, 0, dotv) - f4);
f5 += $omega * (f_eq(w[5], d,v, 1, 0, dotv) - f5);
f6 += $omega * (f_eq(w[6], d,v,-1,-1, dotv) - f6);
f7 += $omega * (f_eq(w[7], d,v, 0,-1, dotv) - f7);
f8 += $omega * (f_eq(w[8], d,v, 1,-1, dotv) - f8);
f_a[0*$nCells + gid] = f0;
f_a[1*$nCells + gid] = f1;
f_a[2*$nCells + gid] = f2;
f_a[3*$nCells + gid] = f3;
f_a[4*$nCells + gid] = f4;
f_a[5*$nCells + gid] = f5;
f_a[6*$nCells + gid] = f6;
f_a[7*$nCells + gid] = f7;
f_a[8*$nCells + gid] = f8;
moments[0*$nCells + gid] = d;
moments[1*$nCells + gid] = v.x;
moments[2*$nCells + 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)] = 2
else:
self.np_material[self.idx(x,y)] = 1
for x in range(1,self.nX-1):
self.np_material[self.idx(x,1)] = 3
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,
'omega': 1.0/0.56
})).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();
velocity = numpy.ndarray(shape=(self.nY-2, self.nX-2))
for y in range(1,self.nY-1):
for x in range(1,self.nX-1):
velocity[y-1,x-1] = numpy.sqrt(self.np_moments[1,self.idx(x,y)]**2 + self.np_moments[2,self.idx(x,y)]**2)
plt.imshow(velocity, cmap=plt.get_cmap("seismic"))
plt.savefig("result/velocity_" + str(i) + ".png")
def MLUPS(cells, steps, time):
return cells * steps / time * 1e-6
nUpdates = 100000
nStat = 1000
print("Initializing simulation...\n")
LBM = D2Q9_BGK_Lattice(256, 256)
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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