import pyopencl as cl mf = cl.mem_flags from pyopencl.tools import get_gl_sharing_context_properties 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. }; uint2 cellAtGid(unsigned int gid) { const int y = gid / $nX; return (uint2)(gid - $nX*y, y); } unsigned int gidOfCell(int x, int y) { return y * $nX + x; } unsigned int indexOfDirection(int i, int j) { return 3*(i+1) + (j+1); } float pop(__global float* cell, int i, int j) { return cell[indexOfDirection(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 norm(float2 v) { return sqrt(dot(v,v)); } float density(__global float* cell) { float d = 0.; for ( int i = 0; i < 9; ++i ) { d += cell[i]; } return d; } float2 velocity(__global float* cell, float d) { return (float2)( (pop(cell,1,0) - pop(cell,-1,0) + pop(cell,1,1) - pop(cell,-1,-1) + pop(cell,1,-1) - pop(cell,-1,1)) / d, (pop(cell,0,1) - pop(cell,0,-1) + pop(cell,1,1) - pop(cell,-1,-1) - pop(cell,1,-1) + pop(cell,-1,1)) / d ); } float equilibrium(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*sq(norm(v))); } __kernel void collide_and_stream(__global float* pop_a, __global float* pop_b, __global int* material) { const unsigned int gid = get_global_id(0); const uint2 cell = cellAtGid(gid); float d = density(&pop_b[gid*9]); float2 v = velocity(&pop_b[gid*9],d); const int m = material[gid]; for ( int i = -1; i <= 1; ++i ) { for ( int j = -1; j <= 1; ++j ) { pop_a[gidOfCell(cell.x+m*i, cell.y+m*j)*9 + indexOfDirection(m*i,m*j)] = pop_b[gid*9 + indexOfDirection(i,j)] + $tau * (equilibrium(d,v,i,j) - pop_b[gid*9 + indexOfDirection(i,j)]); } } }""" 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=(self.nCells, 9), dtype=numpy.float32) self.np_pop_b = numpy.ndarray(shape=(self.nCells, 9), 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.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[:,:] = [ 1./36., 1./9., 1./36., 1./9. , 4./9., 1./9. , 1./36 , 1./9., 1./36. ] self.np_pop_b[:,:] = [ 1./36., 1./9., 1./36., 1./9. , 4./9., 1./9. , 1./36 , 1./9., 1./36. ] 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.nCells,), None, self.cl_pop_a, self.cl_pop_b, self.cl_material) self.queue.finish() else: self.tick = True self.program.collide_and_stream(self.queue, (self.nCells,), None, self.cl_pop_b, self.cl_pop_a, self.cl_material) self.queue.finish() def show(self, i): if self.tick: cl.enqueue_copy(LBM.queue, LBM.np_pop_a, LBM.cl_pop_b).wait(); else: cl.enqueue_copy(LBM.queue, LBM.np_pop_a, LBM.cl_pop_a).wait(); pop = numpy.ndarray(shape=(self.nX, self.nY)) for y in range(0,self.nY-1): for x in range(0,self.nX-1): pop[x,y] = numpy.sum(self.np_pop_a[self.idx(x,y),:]) plt.imshow(pop, vmin=0.2, vmax=2, 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 = 100 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)))