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-rw-r--r--symbolic/D2Q9.py45
1 files changed, 29 insertions, 16 deletions
diff --git a/symbolic/D2Q9.py b/symbolic/D2Q9.py
index a3c2503..8d42245 100644
--- a/symbolic/D2Q9.py
+++ b/symbolic/D2Q9.py
@@ -9,29 +9,42 @@ w = [ Rational(*x) for x in [(1,36), (1,9), (1,36), (1,9), (4,9), (1,9), (1,36),
c_s = sqrt(Rational(1,3))
-rho, tau = symbols('rho tau')
-
f_next = symarray('f_next', q)
f_curr = symarray('f_curr', q)
-u = Matrix(symarray('u', d))
+def moments(f = f_curr, optimize = True):
+ rho = symbols('rho')
+ u = Matrix(symarray('u', d))
+
+ exprs = [ Assignment(rho, sum(f)) ]
+
+ for i, u_i in enumerate(u):
+ exprs.append(Assignment(u_i, sum([ (c_j*f[j])[i] for j, c_j in enumerate(c) ]) / sum(f)))
-moments = [ Assignment(rho, sum(f_curr)) ]
+ if optimize:
+ return cse(exprs, optimizations='basic', symbols=numbered_symbols(prefix='m'))
+ else:
+ return ([], exprs)
-for i, u_i in enumerate(u):
- moments.append(Assignment(u_i, sum([ (c_j*f_curr[j])[i] for j, c_j in enumerate(c) ]) / sum(f_curr)))
+def equilibrium():
+ rho = symbols('rho')
+ u = Matrix(symarray('u', d))
-moments_opt = cse(moments, optimizations='basic', symbols=numbered_symbols(prefix='m'))
+ f_eq = []
-f_eq = []
+ for i, c_i in enumerate(c):
+ f_eq_i = w[i] * rho * ( 1
+ + c_i.dot(u) / c_s**2
+ + c_i.dot(u)**2 / (2*c_s**4)
+ - u.dot(u) / (2*c_s**2) )
+ f_eq.append(f_eq_i)
-for i, c_i in enumerate(c):
- f_eq_i = w[i] * rho * ( 1
- + c_i.dot(u) / c_s**2
- + c_i.dot(u)**2 / (2*c_s**4)
- - u.dot(u) / (2*c_s**2) )
- f_eq.append(f_eq_i)
+ return f_eq
-collide = [ Assignment(f_next[i], f_curr[i] + 1/tau * ( f_eq_i - f_curr[i] )) for i, f_eq_i in enumerate(f_eq) ]
+def bgk(tau, f_eq = equilibrium(), optimize = True):
+ exprs = [ Assignment(f_next[i], f_curr[i] + 1/tau * ( f_eq_i - f_curr[i] )) for i, f_eq_i in enumerate(f_eq) ]
-collide_opt = cse(collide, optimizations='basic')
+ if optimize:
+ return cse(exprs, optimizations='basic')
+ else:
+ return ([], exprs)