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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)))
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