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)