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solver.py
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150 lines (115 loc) · 2.79 KB
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#Dependencies: None
"""
/***************************************************************************
Author :Charles Brissac
Email :cdbrissac (at) gmail.com
License :Apache 2.0
***************************************************************************/
"""
import copy
import random
N=64
visc=0.0
diff=0.0
dt=0.1
def print_array(x):
for i in range(1,N+1):
for j in range(1,N+1):
#print "(%d,%d) "%(i,j),
print("%f "%x[IX(i,j)]),
print('')
print('')
def IX(i,j):
return ((i)+(N+2)*(j))
def SWAP(x0,x):
tmp=x0
x0=x
x=tmp
return x0,x
def set_bnd(b,x):
for i in range(1,N+1):
if b==0:
x[IX(0 ,i)] = x[IX(1,i)]
x[IX(N+1,i)] = x[IX(N,i)]
x[IX(i,0 )] = x[IX(i,1)]
x[IX(i,N+1)] = x[IX(i,N)]
elif b==1:
x[IX(0 ,i)]=-x[IX(1,i)]
x[IX(N+1,i)]=-x[IX(N,i)]
x[IX(i,0 )]=x[IX(i,1)]
x[IX(i,N+1)]=x[IX(i,N)]
elif b==2:
x[IX(0 ,i)]=x[IX(1,i)]
x[IX(N+1,i)]=x[IX(N,i)]
x[IX(i,0 )]=-x[IX(i,1)]
x[IX(i,N+1)]=-x[IX(i,N)]
x[IX(0 ,0 )] = 0.5*(x[IX(1,0 )]+x[IX(0 ,1)]);
x[IX(0 ,N+1)] = 0.5*(x[IX(1,N+1)]+x[IX(0 ,N)]);
x[IX(N+1,0 )] = 0.5*(x[IX(N,0 )]+x[IX(N+1,1)]);
x[IX(N+1,N+1)] = 0.5*(x[IX(N,N+1)]+x[IX(N+1,N)]);
def add_source(x,s):
size=(N+2)*(N+2)
for i in range(size):
x[i] += dt*s[i];
def lin_solve(b,x,x0,a,c):
for k in range(20):
for i in range(1,N+1):
for j in range(1,N+1):
x[IX(i,j)] = (x0[IX(i,j)] + a*(x[IX(i-1,j)]+x[IX(i+1,j)]+x[IX(i,j-1)]+x[IX(i,j+1)]))/c;
set_bnd ( b, x );
def diffuse(b,x,x0):
a=dt*diff*N*N;
lin_solve ( b, x, x0, a, 1+4*a )
def advect(b,d,d0,u,v):
dt0 = dt*N
for i in range(1,N+1):
for j in range(1,N+1):
x=i-dt0*u[IX(i,j)]
y=j-dt0*v[IX(i,j)]
if x<0.5:x=0.5
if x>N+0.5:x=N+0.5
i0=int(x)
i1=i0+1
if y<0.5:y=0.5
if y>N+0.5:y=N+0.5
j0=int(y)
j1=j0+1
s1=x-i0
s0=1-s1
t1=y-j0
t0=1-t1
d[IX(i,j)]=s0*(t0*d0[IX(i0,j0)]+t1*d0[IX(i0,j1)])+s1*(t0*d0[IX(i1,j0)]+t1*d0[IX(i1,j1)])
set_bnd ( b, d )
def project(u,v,p,div):
for i in range(1,N+1):
for j in range(1,N+1):
div[IX(i,j)] = -0.5*(u[IX(i+1,j)]-u[IX(i-1,j)]+v[IX(i,j+1)]-v[IX(i,j-1)])/N;
p[IX(i,j)] = 0.;
set_bnd( 0, div )
set_bnd( 0, p )
lin_solve( 0, p, div, 1, 4 )
for i in range(1,N+1):
for j in range(1,N+1):
u[IX(i,j)] -= 0.5*N*(p[IX(i+1,j)]-p[IX(i-1,j)])
v[IX(i,j)] -= 0.5*N*(p[IX(i,j+1)]-p[IX(i,j-1)])
set_bnd( 1, u )
set_bnd( 2, v )
def velocity_step( u, v, u0, v0 ):
#u0[IX(33,33)]=5.-10.*random.random()
v0[IX(int(N/2+1),int(N/2+1))]=5.
add_source ( u, u0 )
add_source ( v, v0 )
#print_array(u)
if diff>0:
u0,u=SWAP(u0,u)
diffuse( 1, u, u0 )
v0,v=SWAP(v0,v)
diffuse( 2, v, v0 )
project( u, v, u0, v0 )
#print_array(u)
u0,u=SWAP(u0,u)
v0,v=SWAP(v0,v)
advect( 1, u, u0, u0, v0 )
advect( 2, v, v0, u0, v0 )
project( u, v, u0, v0 )
return u,v,u0,v0