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 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 = 2*f_curr_0; const float x2 = 2*f_curr_8; const float x3 = -f_curr_3 + f_curr_5; const float x4 = pow(x0, -2); const float x5 = 9*x4; const float x6 = f_curr_0 - f_curr_8; const float x7 = f_curr_1 - f_curr_7; const float x8 = f_curr_2 - f_curr_6; const float x9 = x6 + x7 + x8; const float x10 = 6/x0; const float x11 = x10*x9; const float x12 = f_curr_3 - f_curr_5; const float x13 = -f_curr_2 + f_curr_6 + x12 + x6; const float x14 = pow(x13, 2); const float x15 = 3*x4; const float x16 = -x14*x15 + 2; const float x17 = x11 + x16; const float x18 = pow(x9, 2); const float x19 = x15*x18; const float x20 = -x19; const float x21 = x10*x13; const float x22 = x20 + x21; const float x23 = 1.0/$tau; const float x24 = (1.0/72.0)*x23; const float x25 = 6*x4; const float x26 = x18*x25; const float x27 = (1.0/18.0)*x23; const float x28 = x5*pow(2*f_curr_2 - 2*f_curr_6 + x3 + x7, 2); const float x29 = x20 - x21; const float x30 = x14*x25 + 2; const float x31 = -f_curr_0 + f_curr_8 + x3 + x8; const float x32 = x15*pow(x31, 2) - 2; const float x33 = x19 + x32; f_a[0*$nCells + gid] = f_curr_0 - x24*(72*f_curr_0 - x0*(x17 + x22 + x5*pow(-f_curr_1 + f_curr_7 - x1 + x2 + x3, 2))); f_a[1*$nCells + gid] = f_curr_1 - x27*(18*f_curr_1 - x0*(x17 + x26)); f_a[2*$nCells + gid] = f_curr_2 - x24*(72*f_curr_2 - x0*(x17 + x28 + x29)); f_a[3*$nCells + gid] = f_curr_3 - x27*(18*f_curr_3 - x0*(x22 + x30)); f_a[4*$nCells + gid] = f_curr_4 - 1.0/9.0*x23*(9*f_curr_4 + 2*x0*x33); f_a[5*$nCells + gid] = f_curr_5 - x27*(18*f_curr_5 - x0*(x29 + x30)); f_a[6*$nCells + gid] = f_curr_6 - x24*(72*f_curr_6 + x0*(x10*x31 + x11 - x28 + x33)); f_a[7*$nCells + gid] = f_curr_7 - x27*(18*f_curr_7 + x0*(x11 - x26 + x32)); f_a[8*$nCells + gid] = f_curr_8 - x24*(72*f_curr_8 - x0*(-x11 + x16 + x29 + x5*pow(x1 + x12 - x2 + x7, 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.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 * 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)