import pyopencl as cl mf = cl.mem_flags import numpy import time import matplotlib import matplotlib.pyplot as plt matplotlib.use('AGG') from sympy import * from sympy.codegen.ast import Assignment from mako.template import Template q = 9 d = 2 c = [ Matrix(x) for x in [(-1, 1), ( 0, 1), ( 1, 1), (-1, 0), ( 0, 0), ( 1, 0), (-1,-1), ( 0, -1), ( 1, -1)] ] w = [ Rational(*x) for x in [(1,36), (1,9), (1,36), (1,9), (4,9), (1,9), (1,36), (1,9), (1,36)] ] c_s = sqrt(Rational(1,3)) rho, tau = symbols('rho tau') f_next = symarray('f_next', q) f_curr = symarray('f_curr', q) u = Matrix(symarray('u', d)) moments = [ Assignment(rho, sum(f_curr)) ] for i, u_i in enumerate(u): moments.append(Assignment(u_i, sum([ (c_j*f_curr[j])[i] for j, c_j in enumerate(c) ]) / sum(f_curr))) moments_opt = cse(moments, optimizations='basic', symbols=numbered_symbols(prefix='m')) f_eq = [] for i, c_i in enumerate(c): f_eq_i = w[i] * rho * ( 1 + c_i.dot(u) / c_s**2 + c_i.dot(u)**2 / (2*c_s**4) - u.dot(u) / (2*c_s**2) ) f_eq.append(f_eq_i) collide = [ Assignment(f_next[i], f_curr[i] + 1/tau * ( f_eq_i - f_curr[i] )) for i, f_eq_i in enumerate(f_eq) ] collide_opt = cse(collide, optimizations='basic') kernel = """ __constant float tau = ${tau}; 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 __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; } % for i, c_i in enumerate(c): const float f_curr_${i} = f_i(f_b, cell.x-(${c_i[0]}), cell.y-(${c_i[1]}), ${c_i[0]}, ${c_i[1]}); % endfor % for i, expr in enumerate(moments_helper): const float ${expr[0]} = ${ccode(expr[1])}; % endfor % for i, expr in enumerate(moments_assignment): float ${ccode(expr)} % endfor if ( m == 2 ) { u_0 = 0.0; u_1 = 0.0; } % for i, expr in enumerate(collide_helper): const float ${expr[0]} = ${ccode(expr[1])}; % endfor % for i, expr in enumerate(collide_assignment): const float ${ccode(expr)} % endfor % for i in range(0,len(c)): f_a[${i*nCells} + gid] = f_next_${i}; % endfor } __kernel void collect_moments(__global __read_only float* f, __global __write_only float* moments) { const unsigned int gid = indexOfCell(get_global_id(0), get_global_id(1)); const uint2 cell = (uint2)(get_global_id(0), get_global_id(1)); % for i in range(0,len(c)): const float f_curr_${i} = f[${i*nCells} + gid]; % endfor % for i, expr in enumerate(moments_helper): const float ${expr[0]} = ${ccode(expr[1])}; % endfor % for i, expr in enumerate(moments_assignment): moments[${i*nCells} + gid] = ${ccode(expr.rhs)}; % endfor }""" 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.np_stat_moments = [] 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).render( nX = self.nX, nY = self.nY, nCells = self.nCells, tau = '0.8f', moments_helper = moments_opt[0], moments_assignment = moments_opt[1], collide_helper = collide_opt[0], collide_assignment = collide_opt[1], c = c, ccode = ccode )).build() def collect_moments(self): if self.tick: self.program.collect_moments(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_b, self.cl_moments) else: self.program.collect_moments(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_a, self.cl_moments) cl.enqueue_copy(LBM.queue, self.np_moments, LBM.cl_moments).wait(); self.np_stat_moments.append(self.np_moments.copy()) def evolve(self): if self.tick: self.tick = False self.program.collide_and_stream(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_a, self.cl_pop_b, self.cl_material) else: self.tick = True self.program.collide_and_stream(self.queue, (self.nX,self.nY), (32,1), self.cl_pop_b, self.cl_pop_a, self.cl_material) def sync(self): self.queue.finish() def generate_moment_plots(self): for i, np_moments in enumerate(self.np_stat_moments): print("Generating plot %d of %d." % (i+1, len(self.np_stat_moments))) 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] = np_moments[0,self.idx(x,y)] plt.figure(figsize=(10, 10)) plt.imshow(density, vmin=0.2, vmax=2.0, cmap=plt.get_cmap("seismic")) plt.savefig("result/density_" + str(i) + ".png", bbox_inches='tight', pad_inches=0) self.np_stat_moments = [] 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): LBM.evolve() if i % nStat == 0: LBM.sync() print("i = %4d; %3.0f MLUPS" % (i, MLUPS(LBM.nCells, nStat, time.time() - lastStat))) LBM.collect_moments() lastStat = time.time() print("\nConcluded simulation.\n") LBM.generate_moment_plots()