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ZouHeBC.py
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ZouHeBC.py
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from bearded_octo_wookie.lbm import *
from sympy import *
from fractions import Fraction
from bearded_octo_wookie.MRT import genFeq, getMRT
from sympy.utilities.codegen import codegen
#W = np.array([Rational(_W) / Rational(36) for _W in W[:] * 36.])
U = [var('U_0'), var('U_1')]
rho = var('rho')
D = 2
Q = 9
def getUBc(wall_e, ux, uy, verbose=False):
eqs = list()
feq = genFeq(e)
meq, M = getMRT(e)
t = 'f_0'
t2 = 'if_0'
for i in range(1,Q):
t = t + ',f_'+str(i)
t2 = t2 + ',if_'+str(i)
fs = np.array(var(t))
ifs = np.array(var(t2))
### incoming
i_known = list()
i_unknown = list()
unknowns = list()
for i in range(1,Q):
if e[i][0]*wall_e[0] + e[i][1]*wall_e[1] <= 0:
fs[i] = ifs[i]
i_known.append(i)
else:
unknowns.append(fs[i])
i_unknown.append(i)
fs[0] = ifs[0]
i_known.append(0)
m = M.dot(fs)
meq = M.dot(feq)
for i in range(3):
eqs.append(meq[i] - m[i])
### NORMAL PART REFLECTION
for i in range(1,Q):
for i2 in range(1,Q):
if ( e[i][0] + wall_e[0] == 0 and e[i][1] + wall_e[1] == 0 ) \
and ( e[i][0] + e[i2][0] == 0 and e[i][1] + e[i2][1] == 0 ):
eqs.append(fs[i] - feq[i] - (fs[i2] - feq[i2]))
unknowns.append(rho)
sol = solve(eqs, unknowns)
if verbose:
for s in sol:
pprint(s)
pprint(sol[s])
print "WWWWWWWWWWWWWWWWWW " + str(s) + " WWWWWWWWWWWWWWWWWWWW"
print ccode(sol[s], s)
print "WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW"
A = np.zeros((9,10)).tolist()
for i in range(Q):
if i in i_known:
A[i][i] = 1
elif i in i_unknown:
eq = sol[ fs[i] ]
for i2 in range(Q):
A[i][i2] = expand(eq).coeff(ifs[i2])
eq = expand(eq - A[i][i2] * ifs[i2])
A[i][9] = eq
f = lambdify(U, A)
return lambda x,y : np.array(f(x,y), dtype=float), np.array(f(ux,uy), dtype=float)
def getRhoBc(wall_e, rhobc, Utbc = 0.):
eqs = list()
feq = genFeq(e)
meq, M = getMRT(e)
t = 'f_0'
t2 = 'if_0'
for i in range(1,Q):
t = t + ',f_'+str(i)
t2 = t2 + ',if_'+str(i)
fs = np.array(var(t))
ifs = np.array(var(t2))
### incoming
i_known = list()
i_unknown = list()
unknowns = list()
for i in range(1,Q):
if e[i][0]*wall_e[0] + e[i][1]*wall_e[1] <= 0:
fs[i] = ifs[i]
i_known.append(i)
else:
unknowns.append(fs[i])
i_unknown.append(i)
fs[0] = ifs[0]
i_known.append(0)
m = M.dot(fs)
meq = M.dot(feq)
for i in range(3):
eqs.append(meq[i] - m[i])
### NORMAL PART REFLECTION
for i in range(1,Q):
for i2 in range(1,Q):
if ( e[i][0] + wall_e[0] == 0 and e[i][1] + wall_e[1] == 0 ) \
and ( e[i][0] + e[i2][0] == 0 and e[i][1] + e[i2][1] == 0 ):
eqs.append(fs[i] - feq[i] - (fs[i2] - feq[i2]))
wall_e_t = np.array(var("x1,y1"))
wall_e_t = solve([wall_e_t.dot(wall_e), wall_e_t.dot(wall_e_t) - 1.] , wall_e_t.tolist())
wall_e_t = np.array(wall_e_t[0])
wall_e = np.array(wall_e)
Un = var("Un")
Ut = var("Ut")
eqs.append( wall_e.dot(U) - Un )
eqs.append(wall_e_t.dot(U) + Ut)
unknowns.append(Un)
unknowns.append(U[0])
unknowns.append(U[1])
sol = solve(eqs, unknowns)
A = np.zeros((9,10)).tolist()
for i in range(Q):
if i in i_known:
A[i][i] = 1
elif i in i_unknown:
eq = sol[ fs[i] ]
for i2 in range(Q):
A[i][i2] = expand(eq).coeff(ifs[i2])
eq = expand(eq - A[i][i2] * ifs[i2])
A[i][9] = eq
f = lambdify([rho,Ut], A)
return lambda x, y : np.array(f(x,y), dtype=float), np.array(f(rhobc, Utbc), dtype=float)
def getDNBc(wall_e):
eqs = list()
feq = genFeq(e)
meq, M = getMRT(e)
t = 'f_0'
t2 = 'if_0'
for i in range(1,Q):
t = t + ',f_'+str(i)
t2 = t2 + ',if_'+str(i)
fs = np.array([var('f_'+str(i)) for i in range(9)])
ifs = np.array([var('if_'+str(i)) for i in range(9)])
### incoming
i_known = list()
i_unknown = list()
unknowns = list()
for i in range(1,Q):
if e[i][0]*wall_e[0] + e[i][1]*wall_e[1] <= 0:
fs[i] = ifs[i]
i_known.append(i)
else:
unknowns.append(fs[i])
i_unknown.append(i)
fs[0] = ifs[0]
i_known.append(0)
m = M.dot(fs)
meq = M.dot(feq)
P = np.zeros((2,2)).tolist()
for k, v in enumerate(e):
Pij = np.array([ [v[j] * v[i] * ( feq[k] - fs[k] ) for j in range(2)] for i in range(2) ])
P = np.array(P) + Pij
Pn = P.dot(wall_e)
eqs.append(m[0] - rho)
eqs.append(m[1] - U[0] * rho)
eqs.append(m[2] - U[1] * rho)
### NORMAL PART REFLECTION
# for i in range(1,Q):
# for i2 in range(1,Q):
# if ( e[i][0] + wall_e[0] == 0 and e[i][1] + wall_e[1] == 0 ) \
# and ( e[i][0] + e[i2][0] == 0 and e[i][1] + e[i2][1] == 0 ):
# eqs.append(fs[i] - feq[i] - (fs[i2] - feq[i2]))
#
#
# ux = 1.
# uy = 1.
print eqs
print unknowns
sol = solve(eqs, unknowns)
print sol
A = np.zeros((9,10)).tolist()
for i in range(Q):
if i in i_known:
A[i][i] = 1
elif i in i_unknown:
eq = sol[ fs[i] ]
for i2 in range(Q):
A[i][i2] = expand(eq).coeff(ifs[i2])
eq = expand(eq - A[i][i2] * ifs[i2])
A[i][9] = eq
f = lambdify((rho,U[0],U[1]), A)
unknowns = list()
eqs = list()
nu = Rational(1.)/Rational(6.)
eqs.append(Pn[0] - rho*wall_e[0] / nu)
eqs.append(Pn[1] - rho*wall_e[1] / nu)
unknowns.append(U[0])
unknowns.append(U[1])
sol2 = solve(eqs, unknowns)
f2 = lambdify([rho, fs], sol2)
return f, f2
if __name__ == '__main__':
#print getDNBc([0,1])
getUBc([0,1], 0., 0.01, True )
#fA,A = getRhoBc([1,0], 1. )
#
#f0 = W[:]
#f = np.ones(10)
#f[:-1] = f0
#f1 = A.dot(f)
##print f1
#
#rho = np.sum(f1)
#
#U0 = np.zeros(2)
#for i in range(1,9):
# U0[0] = U0[0] + e[i][0]*f1[i]
# U0[1] = U0[1] + e[i][1]*f1[i]
#U0[0] = U0[0] / rho
#U0[1] = U0[1] / rho
#
#print U0