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nscavity.py
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##Cavity Flow Navier Stokes
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
import os
import time
def main(nx):
##variable declarations
flowtime = 0.1
# nx = 256
ny = nx
nit=50
c = 1
dx = 2.0/(nx-1)
dy = 2.0/(ny-1)
x = np.linspace(0,2,nx)
y = np.linspace(0,2,ny)
Y,X = np.meshgrid(y,x)
dt = dx/50
nt = int(flowtime/dt)
##physical variables
rho = 1
nu = .1
u = np.zeros((ny,nx)) ##create a XxY vector of 0's
un = np.zeros((ny,nx)) ##create a XxY vector of 0's
v = np.zeros((ny,nx)) ##create a XxY vector of 0's
vn = np.zeros((ny,nx)) ##create a XxY vector of 0's
p = np.zeros((ny,nx)) ##create a XxY vector of 0's
pn = np.zeros((ny,nx)) ##create a XxY vector of 0's
b = np.zeros((ny,nx))
t1 = time.time()
for n in range(nt):
un[:] = u[:]
vn[:] = v[:]
b[1:-1,1:-1]=rho*(1/dt*((u[2:,1:-1]-u[0:-2,1:-1])/(2*dx)+(v[1:-1,2:]-v[1:-1,0:-2])/(2*dy))-\
((u[2:,1:-1]-u[0:-2,1:-1])/(2*dx))**2-\
2*((u[1:-1,2:]-u[1:-1,0:-2])/(2*dy)*(v[2:,1:-1]-v[0:-2,1:-1])/(2*dx))-\
((v[1:-1,2:]-v[1:-1,0:-2])/(2*dy))**2)
for q in range(nit):
pn[:] = p[:]
p[1:-1,1:-1] = ((pn[2:,1:-1]+pn[0:-2,1:-1])*dy**2+(pn[1:-1,2:]+pn[1:-1,0:-2])*dx**2)/\
(2*(dx**2+dy**2)) -\
dx**2*dy**2/(2*(dx**2+dy**2))*b[1:-1,1:-1]
p[-1,:] =p[-2,:] ##p = 0 at y = 2
p[0,:] = p[1,:] ##dp/dy = 0 at y = 0
p[:,0]=p[:,1] ##dp/dx = 0 at x = 0
p[:,-1]=0 ##dp/dx = 0 at x = 2
u[1:-1,1:-1] = un[1:-1,1:-1]-\
un[1:-1,1:-1]*dt/dx*(un[1:-1,1:-1]-un[0:-2,1:-1])-\
vn[1:-1,1:-1]*dt/dy*(un[1:-1,1:-1]-un[1:-1,0:-2])-\
dt/(2*rho*dx)*(p[2:,1:-1]-p[0:-2,1:-1])+\
nu*(dt/dx**2*(un[2:,1:-1]-2*un[1:-1,1:-1]+un[0:-2,1:-1])+\
dt/dy**2*(un[1:-1,2:]-2*un[1:-1,1:-1]+un[1:-1,0:-2]))
v[1:-1,1:-1] = vn[1:-1,1:-1]-\
un[1:-1,1:-1]*dt/dx*(vn[1:-1,1:-1]-vn[0:-2,1:-1])-\
vn[1:-1,1:-1]*dt/dy*(vn[1:-1,1:-1]-vn[1:-1,0:-2])-\
dt/(2*rho*dy)*(p[1:-1,2:]-p[1:-1,0:-2])+\
nu*(dt/dx**2*(vn[2:,1:-1]-2*vn[1:-1,1:-1]+vn[0:-2,1:-1])+\
(dt/dy**2*(vn[1:-1,2:]-2*vn[1:-1,1:-1]+vn[1:-1,0:-2])))
u[0,:] = 0
u[:,0] = 0
u[:,-1] = 1
v[0,:] = 0
v[-1,:]=0
v[:,0] = 0
v[:,-1] = 0
u[-1,:] = 0 ## at y = 2 where u = 1
t2 = time.time()
print t2-t1
f = open('numpycavity0.1','a')
f.write(str(nx) + '\n')
f.write(str(nx**2) + '\n')
f.write(str(t2-t1) + '\n')
f.write(str(dt) + '\n')
f.write(str(nt) + '\n')
f.close()
#
#prescon = plt.figure()
#plt.contourf(X,Y,p,alpha=0.5)
#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')
#
#stream = plt.figure()
#plt.streamplot(x,y,np.transpose(u),np.transpose(v),density=[5, 2])
#plt.contourf(X,Y,p,alpha=0.5)
#plt.colorbar()
#plt.xlabel('X')
#plt.ylabel('Y')
#plt.title('Velocity field streamplot')
plt.ion()
anicheck = raw_input('Do you want to animate the results?(y/n): ')
##variable declarations
nx = 41
ny = 41
nt = 500
nit=50
c = 1
dx = 2.0/(nx-1)
dy = 2.0/(ny-1)
x = np.linspace(0,2,nx)
y = np.linspace(0,2,ny)
Y,X = np.meshgrid(y,x)
##physical variables
rho = 1
nu = .1
dt = .001
#dt = input('Enter dt: ')
u = np.zeros((ny,nx)) ##create a XxY vector of 0's
un = np.zeros((ny,nx)) ##create a XxY vector of 0's
v = np.zeros((ny,nx)) ##create a XxY vector of 0's
vn = np.zeros((ny,nx)) ##create a XxY vector of 0's
p = np.zeros((ny,nx)) ##create a XxY vector of 0's
pn = np.zeros((ny,nx)) ##create a XxY vector of 0's
b = np.zeros((ny,nx))
plt.figure()
for n in range(nt):
un[:] = u[:]
vn[:] = v[:]
b[1:-1,1:-1]=rho*(1/dt*((u[2:,1:-1]-u[0:-2,1:-1])/(2*dx)+(v[1:-1,2:]-v[1:-1,0:-2])/(2*dy))-\
((u[2:,1:-1]-u[0:-2,1:-1])/(2*dx))**2-\
2*((u[1:-1,2:]-u[1:-1,0:-2])/(2*dy)*(v[2:,1:-1]-v[0:-2,1:-1])/(2*dx))-\
((v[1:-1,2:]-v[1:-1,0:-2])/(2*dy))**2)
for q in range(nit):
pn[:] = p[:]
p[1:-1,1:-1] = ((pn[2:,1:-1]+pn[0:-2,1:-1])*dy**2+(pn[1:-1,2:]+pn[1:-1,0:-2])*dx**2)/\
(2*(dx**2+dy**2)) -\
dx**2*dy**2/(2*(dx**2+dy**2))*b[1:-1,1:-1]
p[-1,:] =p[-2,:] ##p = 0 at y = 2
p[0,:] = p[1,:] ##dp/dy = 0 at y = 0
p[:,0]=p[:,1] ##dp/dx = 0 at x = 0
p[:,-1]=0 ##dp/dx = 0 at x = 2
u[1:-1,1:-1] = un[1:-1,1:-1]-\
un[1:-1,1:-1]*dt/dx*(un[1:-1,1:-1]-un[0:-2,1:-1])-\
vn[1:-1,1:-1]*dt/dy*(un[1:-1,1:-1]-un[1:-1,0:-2])-\
dt/(2*rho*dx)*(p[2:,1:-1]-p[0:-2,1:-1])+\
nu*(dt/dx**2*(un[2:,1:-1]-2*un[1:-1,1:-1]+un[0:-2,1:-1])+\
dt/dy**2*(un[1:-1,2:]-2*un[1:-1,1:-1]+un[1:-1,0:-2]))
v[1:-1,1:-1] = vn[1:-1,1:-1]-\
un[1:-1,1:-1]*dt/dx*(vn[1:-1,1:-1]-vn[0:-2,1:-1])-\
vn[1:-1,1:-1]*dt/dy*(vn[1:-1,1:-1]-vn[1:-1,0:-2])-\
dt/(2*rho*dy)*(p[1:-1,2:]-p[1:-1,0:-2])+\
nu*(dt/dx**2*(vn[2:,1:-1]-2*vn[1:-1,1:-1]+vn[0:-2,1:-1])+\
(dt/dy**2*(vn[1:-1,2:]-2*vn[1:-1,1:-1]+vn[1:-1,0:-2])))
u[0,:] = 0
u[:,0] = 0
u[:,-1] = 1
v[0,:] = 0
v[-1,:]=0
v[:,0] = 0
v[:,-1] = 0
u[-1,:] = 0 ## at y = 2 where u = 1
if anicheck=='y' and n%5==0:
plt.clf()
plt.contourf(X,Y,p)
plt.quiver(X,Y,u,v)
plt.draw()
if anicheck=='n':
plt.close()
prescon = plt.figure()
plt.contourf(X,Y,p,alpha=0.5)
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')
stream = plt.figure()
plt.streamplot(x,y,np.transpose(u),np.transpose(v),density=[5, 2])
plt.contourf(X,Y,p,alpha=0.5)
plt.colorbar()
plt.xlabel('X')
plt.ylabel('Y')
plt.title('Velocity field streamplot')