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gpu_cavity.py
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gpu_cavity.py
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import numpy
from numbapro import autojit, cuda, jit, float32
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import math
import time
################################################################################
################################################################################
################################################################################
### This code requires NumbaPro, available from Continuum Analytics (continuum.io)
### and an NVIDIA GPU with Cuda 5.0 and a compute capability >= 2.0
################################################################################
################################################################################
################################################################################
###Decorator to tell NumbaPro to compile the following function into a CUDA kernel
@jit(argtypes=[float32[:,:], float32[:,:], float32[:,:], float32[:,:], float32[:,:], float32, float32, float32, float32, float32], target='gpu')
def CudaU(U, V, P, UN, VN, dx, dy, dt, rho, nu):
###Retrieve thread ID, block ID and block dimension for both x & y
tidx = cuda.threadIdx.x
blkidx = cuda.blockIdx.x
blkdimx = cuda.blockDim.x
tidy = cuda.threadIdx.y
blkidy = cuda.blockIdx.y
blkdimy = cuda.blockDim.y
m, n = U.shape
###Given thread ID, block ID and block dim, calculate corresponding i & j on grid
i = tidx + blkidx * blkdimx
j = tidy + blkidy * blkdimy
if i >= U.shape[0] or j >= U.shape[1]:
return ###if you try to index out of the array bounds, kill the thread
####Calculate U velocity
UN[i,j]=U[i,j]-U[i,j]*dt/dx*(U[i,j]-U[i-1,j])-\
V[i,j]*dt/dy*(U[i,j]-U[i,j-1])-\
dt/(2*rho*dx)*(P[i+1,j]-P[i-1,j])+\
nu*(dt/dx**2*(U[i+1,j]-2*U[i,j]+U[i-1,j])+\
dt/dy**2*(U[i,j+1]-2*U[i,j]+U[i,j-1]))
####Implement B.C. for U
if i == 0:
UN[i, j] = 0
elif i == m-1:
UN[i, j] = 0
elif j == 0:
UN[i, j] = 0
elif j == n-1:
UN[i, j] = 1
####Calculate V velocity
VN[i,j]=V[i,j]-U[i,j]*dt/dx*(V[i,j]-V[i-1,j])-\
V[i,j]*dt/dy*(V[i,j]-V[i,j-1])-\
dt/(2*rho*dx)*(P[i,j+1]-P[i,j-1])+\
nu*(dt/dx**2*(V[i+1,j]-2*V[i,j]+V[i-1,j])+\
dt/dy**2*(V[i,j+1]-2*V[i,j]+V[i,j-1]))
####Implement B.C. for V
if i == 0:
VN[i, j] = 0
elif i == m-1:
VN[i, j] = 0
elif j == 0:
VN[i, j] = 0
elif j == n-1:
VN[i, j] = 0
####Copy updated values back to original U and V arrays before transfer off GPU
U[i,j] = UN[i,j]
V[i,j] = VN[i,j]
@autojit ###Target the following function for CPU vectorization (possible speed gains to be had by specifying variable inputs
def ppe(rho, dt, dx, dy, U, V, P):
height, width = U.shape
B = numpy.zeros((height, width))
PN = numpy.zeros((height, width))
nit = 50
for i in range(1,width-1):
for j in range(1, height-1):
B[i,j] = 1/dt*((U[i+1,j]-U[i-1,j])/(2*dx)+\
(V[i,j+1]-V[i,j-1])/(2*dy))-\
((U[i+1,j]-U[i-1,j])/(2*dx))**2-\
2*(U[i,j+1]-U[i,j-1])/(2*dy)*\
(V[i+1,j]-V[i-1,j])/(2*dx)-\
((V[i,j+1]-V[i,j-1])/(2*dy))**2
for n in range(nit):
for i in range(1,width-1):
for j in range(1, height-1):
PN[i,j] = ((P[i+1,j]+P[i-1,j])*dy**2+\
(P[i,j+1] + P[i,j-1])*dx**2)/(2*(dx**2+dy**2))\
-rho*dx**2*dy**2/(2*(dx**2+dy**2))*B[i,j]
for i in range(height):
PN[i, 0] = PN[i, 1]
PN[i, width-1] = 0
for j in range(width):
PN[0, j] = PN[1, j]
PN[height-1,j] = PN[height-2, j]
P[:] = PN[:]
return P
def main():
flowtime = 0.1
nx = 128
ny = 128
dx = 2.0/(nx-1)
dy = 2.0/(ny-1)
dt = dx/50 ##ensures stability for a given mesh fineness
rho = 1.0
nu =.1
nt = int(flowtime/dt) ##calculate number of timesteps required to reach a specified total flowtime
U = numpy.zeros((nx,ny), dtype=numpy.float32)
U[-1,:] = 1
V = numpy.zeros((nx,ny), dtype=numpy.float32)
P = numpy.zeros((ny, nx), dtype=numpy.float32)
UN = numpy.zeros((nx,ny), dtype=numpy.float32)
VN = numpy.zeros((nx,ny), dtype=numpy.float32)
griddim = nx, ny
blockdim = 768, 768, 1
#if nx > 767:
# griddim = int(math.ceil(float(nx)/blockdim[0])), int(math.ceil(float(ny)/blockdim[0]))
t1 = time.time()
###Target the GPU to begin calculation
stream = cuda.stream()
d_U = cuda.to_device(U, stream)
d_V = cuda.to_device(V, stream)
d_UN = cuda.to_device(UN, stream)
d_VN = cuda.to_device(VN, stream)
for i in range(nt):
P = ppe(rho, dt, dx, dy, U, V, P)
CudaU[griddim, blockdim, stream](d_U, d_V, P, d_UN, d_VN, dx, dy, dt, rho, nu)
d_U.to_host(stream)
d_V.to_host(stream)
stream.synchronize()
t2 = time.time()
print "Completed grid of %d by %d in %.6f seconds" % (nx, ny, t2-t1)
x = numpy.linspace(0,2,nx)
y = numpy.linspace(0,2,ny)
Y,X = numpy.meshgrid(y,x)
#prescon = plt.figure()
#plt.contourf(X[::10,::10],Y[::10,::10],P[::10,::10],alpha=0.5)
#plt.colorbar()
#plt.contour(X[::10,::10],Y[::10,::10],P[::10,::10])
#plt.quiver(X[::10,::10],Y[::10,::10],U[::10,::10],V[::10,::10])
#plt.xlabel('X')
#plt.ylabel('Y')
#plt.title('Pressure contour')
#plt.contourf(X,Y,P,alpha=.5)
#plt.colorbar()
#plt.contour(X,Y,P,)
#plt.quiver(X[::2,::2],Y[::2,::2],U[::2,::2],V[::2,::2])
#plt.xlabel('X')
#plt.ylabel('Y')
#plt.title('Pressure contour')
#plt.show()
#f = open('cudajit_cavity', 'a')
#f.write(str(nx)+'\n')
#f.write(str(t2-t1) +'\n')
#f.write(str(dt) + '\n')
#f.write(str(nt) + '\n')
#f.close()
# from ghiacompy import plotghiacomp
# plotghiacomp(U[(nx-1)/2,:],numpy.linspace(0,1,ny))
if __name__ == "__main__":
main()