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Alex_spectrum.py
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Alex_spectrum.py
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##------------------------------------
from scipy import *
from scipy.linalg import inv, solve, eig, det
import pickle
##------------------------------------
M = 150
Re = 0
Wi = 10.82
bbeta = 0.1
_delta = 0.14
##------------------------------------
II = identity(M,dtype='d')
cbar = ones(M,dtype='d')
cbar[0] = 2.0
cbar[M-1] = 2.0
ygl = zeros(M,dtype='d')
for m in range(M):
ygl[m] = cos(pi*m/(M-1))
zzz_up = zeros(M,dtype='d')
for m in range(M):
zzz_up[m] = 0.5*(ygl[m]+1.0)
zzz_down = zeros(M,dtype='d')
for m in range(M):
zzz_down[m] = 0.5*(ygl[m]-1.0)
D1 = zeros((M,M),dtype='d')
for l in range(M):
for j in range(M):
if l != j:
D1[l,j] = cbar[l]*((-1)**(l+j))/(cbar[j]*(ygl[l]-ygl[j]))
for j in range(1,M-1):
D1[j,j] = -0.5*ygl[j]/(1.0-ygl[j]*ygl[j])
D1[0,0] = (2.0*(M-1)*(M-1)+1.0)/6.0
D1[M-1,M-1] = -D1[0,0]
D1 = 2*D1
D2 = dot(D1,D1)
## Laminar profile
U0up = zeros(M,dtype='d')
for m in range(M):
U0up[m] = tanh(zzz_up[m]/_delta)/tanh(1.0/_delta)
Txyup = dot(D1,U0up)
Txxup = 2*Wi*Txyup*Txyup
U0up_p = dot(D1,U0up)
U0down = zeros(M,dtype='d')
for m in range(M):
U0down[m] = tanh(zzz_down[m]/_delta)/tanh(1.0/_delta)
Txydown = dot(D1,U0down)
Txxdown = 2*Wi*Txydown*Txydown
U0down_p = dot(D1,U0down)
alpha = 1.57
print alpha
LPL = D2 - alpha*alpha*II
## LHS
## ux[0:M] uy[M:2*M] p[2*M:3*M]
## sxx[3*M:4*M] sxy[4*M:5*M] syy[5*M:6*M]
LHS = zeros((12*M,12*M),dtype='D')
##### Upper half
# NS x
LHS[0:M,0:M] = -Re*1j*alpha*U0up*II + bbeta*LPL
LHS[0:M,M:2*M] = -Re*U0up_p*II
LHS[0:M,2*M:3*M] = -1j*alpha*II
LHS[0:M,3*M:4*M] = (1.0-bbeta)*1j*alpha*II
LHS[0:M,4*M:5*M] = (1.0-bbeta)*D1
# NS y
LHS[M:2*M,M:2*M] = -Re*1j*alpha*U0up*II + bbeta*LPL
LHS[M:2*M,2*M:3*M] = -D1
LHS[M:2*M,4*M:5*M] = (1.0-bbeta)*1j*alpha*II
LHS[M:2*M,5*M:6*M] = (1.0-bbeta)*D1
# Incompressibility
LHS[2*M:3*M,0:M] = 1j*alpha*II
LHS[2*M:3*M,M:2*M] = D1
## Oldroyd-B xx
LHS[3*M:4*M,0:M] = -2*Wi*1j*alpha*Txxup*II - 2*Wi*dot(Txyup*II,D1) - 2*1j*alpha*II
LHS[3*M:4*M,M:2*M] = Wi*dot(D1,Txxup)*II
LHS[3*M:4*M,3*M:4*M] = II + 1j*alpha*Wi*U0up*II
LHS[3*M:4*M,4*M:5*M] = -2*Wi*U0up_p*II
## Oldroyd-B xy
LHS[4*M:5*M,0:M] = -D1
LHS[4*M:5*M,M:2*M] = Wi*dot(D1,Txyup)*II - Wi*1j*alpha*Txxup*II - 1j*alpha*II
LHS[4*M:5*M,4*M:5*M] = II + 1j*alpha*Wi*U0up*II
LHS[4*M:5*M,5*M:6*M] = -Wi*U0up_p*II
## Oldroyd-B yy
LHS[5*M:6*M,M:2*M] = -2*Wi*Txyup*1j*alpha*II - 2*D1
LHS[5*M:6*M,5*M:6*M] = II + 1j*alpha*Wi*U0up*II
##### Lower half
# NS x
LHS[6*M:7*M,6*M:7*M] = -Re*1j*alpha*U0down*II + bbeta*LPL
LHS[6*M:7*M,7*M:8*M] = -Re*U0down_p*II
LHS[6*M:7*M,8*M:9*M] = -1j*alpha*II
LHS[6*M:7*M,9*M:10*M] = (1.0-bbeta)*1j*alpha*II
LHS[6*M:7*M,10*M:11*M] = (1.0-bbeta)*D1
# NS y
LHS[7*M:8*M,7*M:8*M] = -Re*1j*alpha*U0down*II + bbeta*LPL
LHS[7*M:8*M,8*M:9*M] = -D1
LHS[7*M:8*M,10*M:11*M] = (1.0-bbeta)*1j*alpha*II
LHS[7*M:8*M,11*M:12*M] = (1.0-bbeta)*D1
# Incompressibility
LHS[8*M:9*M,6*M:7*M] = 1j*alpha*II
LHS[8*M:9*M,7*M:8*M] = D1
## Oldroyd-B xx
LHS[9*M:10*M,6*M:7*M] = -2*Wi*1j*alpha*Txxdown*II - 2*Wi*dot(Txydown*II,D1) - 2*1j*alpha*II
LHS[9*M:10*M,7*M:8*M] = Wi*dot(D1,Txxdown)*II
LHS[9*M:10*M,9*M:10*M] = II + 1j*alpha*Wi*U0down*II
LHS[9*M:10*M,10*M:11*M] = -2*Wi*U0down_p*II
## Oldroyd-B xy
LHS[10*M:11*M,6*M:7*M] = -D1
LHS[10*M:11*M,7*M:8*M] = Wi*dot(D1,Txydown)*II - Wi*1j*alpha*Txxdown*II - 1j*alpha*II
LHS[10*M:11*M,10*M:11*M] = II + 1j*alpha*Wi*U0down*II
LHS[10*M:11*M,11*M:12*M] = -Wi*U0down_p*II
## Oldroyd-B yy
LHS[11*M:12*M,7*M:8*M] = -2*Wi*Txydown*1j*alpha*II - 2*D1
LHS[11*M:12*M,11*M:12*M] = II + 1j*alpha*Wi*U0down*II
## RHS
RHS = zeros((12*M,12*M),dtype='D')
RHS[0:M,0:M] = Re*II
RHS[M:2*M,M:2*M] = Re*II
RHS[3*M:4*M,3*M:4*M] = -Wi*II
RHS[4*M:5*M,4*M:5*M] = -Wi*II
RHS[5*M:6*M,5*M:6*M] = -Wi*II
RHS[6*M:7*M,6*M:7*M] = Re*II
RHS[7*M:8*M,7*M:8*M] = Re*II
RHS[9*M:10*M,9*M:10*M] = -Wi*II
RHS[10*M:11*M,10*M:11*M] = -Wi*II
RHS[11*M:12*M,11*M:12*M] = -Wi*II
## Boundary conditions
LHS[0] = zeros(12*M,dtype='D')
LHS[M-1] = zeros(12*M,dtype='D')
LHS[M] = zeros(12*M,dtype='D')
LHS[2*M-1] = zeros(12*M,dtype='D')
LHS[6*M] = zeros(12*M,dtype='D')
LHS[7*M-1] = zeros(12*M,dtype='D')
LHS[7*M] = zeros(12*M,dtype='D')
LHS[8*M-1] = zeros(12*M,dtype='D')
LHS[0,0] = 1.0
LHS[M,M] = 1.0
LHS[7*M-1,7*M-1] = 1.0
LHS[8*M-1,8*M-1] = 1.0
LHS[M-1,M-1] = 1.0
LHS[M-1,6*M] = -1.0
LHS[2*M-1,2*M-1] = 1.0
LHS[2*M-1,7*M] = -1.0
#LHS[6*M,0:M] = D1[M-1]
#LHS[6*M,6*M:7*M] = -D1[0]
#LHS[7*M,M:2*M] = D1[M-1]
#LHS[7*M,7*M:8*M] = -D1[0]
LHS[6*M,0:M] = bbeta*D1[M-1]
LHS[6*M,2*M-1] = 1j*alpha*bbeta
LHS[6*M,5*M-1] = (1.0-bbeta)
LHS[6*M,6*M:7*M] = -bbeta*D1[0]
LHS[6*M,7*M] = -1j*alpha*bbeta
LHS[6*M,10*M] = -(1.0-bbeta)
LHS[7*M,M:2*M] = 2*bbeta*D1[M-1]
LHS[7*M,3*M-1] = -1.0
LHS[7*M,6*M-1] = (1.0-bbeta)
LHS[7*M,7*M:8*M] = -2*bbeta*D1[0]
LHS[7*M,8*M] = 1.0
LHS[7*M,11*M] = -(1.0-bbeta)
RHS[0] = zeros(12*M,dtype='D')
RHS[M-1] = zeros(12*M,dtype='D')
RHS[M] = zeros(12*M,dtype='D')
RHS[2*M-1] = zeros(12*M,dtype='D')
RHS[6*M] = zeros(12*M,dtype='D')
RHS[7*M-1] = zeros(12*M,dtype='D')
RHS[7*M] = zeros(12*M,dtype='D')
RHS[8*M-1] = zeros(12*M,dtype='D')
_spec = eig(LHS,RHS,left=0,right=0)
# Save output
eigarray = vstack((real(_spec), imag(_spec))).T
#remove nans and infs from eigenvalues
eigarray = eigarray[~isnan(eigarray).any(1), :]
eigarray = eigarray[~isinf(eigarray).any(1), :]
filename = 'Alex-ev-kx{kx}-M{M}-Re{Re}-beta{beta}-Wi{Weiss}-delta{delta}.dat'.format(
kx=alpha,M=M,Re=Re,beta=bbeta,Weiss=Wi,delta=_delta)
print 'save and exit'
savetxt(filename, eigarray)