diff options
Diffstat (limited to 'symbolic')
| -rw-r--r-- | symbolic/D2Q9.py | 45 |
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) |