1 files changed, 37 insertions, 0 deletions
diff --git a/symbolic/D2Q9.py b/symbolic/D2Q9.py
new file mode 100644
index 0000000..a3c2503
--- /dev/null
+++ b/symbolic/D2Q9.py
@@ -0,0 +1,37 @@
+from sympy import *
+from sympy.codegen.ast import Assignment
+
+q = 9
+d = 2
+
+c = [ Matrix(x) for x in [(-1, 1), ( 0, 1), ( 1, 1), (-1, 0), ( 0, 0), ( 1, 0), (-1,-1), ( 0, -1), ( 1, -1)] ]
+w = [ Rational(*x) for x in [(1,36), (1,9), (1,36), (1,9), (4,9), (1,9), (1,36), (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))
+
+moments = [ Assignment(rho, sum(f_curr)) ]
+
+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)))
+
+moments_opt = cse(moments, optimizations='basic', symbols=numbered_symbols(prefix='m'))
+
+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)
+
+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) ]
+
+collide_opt = cse(collide, optimizations='basic')