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Diffstat (limited to 'symbolic/characteristics.py')
-rw-r--r-- | symbolic/characteristics.py | 21 |
1 files changed, 21 insertions, 0 deletions
diff --git a/symbolic/characteristics.py b/symbolic/characteristics.py new file mode 100644 index 0000000..ca3904e --- /dev/null +++ b/symbolic/characteristics.py @@ -0,0 +1,21 @@ +from sympy import * + +# copy of `sympy.integrals.quadrature.gauss_hermite` sans evaluation +def gauss_hermite(n): + x = Dummy("x") + p = hermite_poly(n, x, polys=True) + p1 = hermite_poly(n-1, x, polys=True) + xi = [] + w = [] + for r in p.real_roots(): + xi.append(r) + w.append(((2**(n-1) * factorial(n) * sqrt(pi))/(n**2 * p1.subs(x, r)**2))) + return xi, w + +# determine weights of a d-dimensional LBM model on velocity set c +# (only works for velocity sets that result into NSE-recovering LB models when +# plugged into Gauss-Hermite quadrature without any additional arguments +# i.e. D2Q9 and D3Q27 but not D3Q19) +def weights(d, c): + _, omegas = gauss_hermite(3) + return list(map(lambda c_i: Mul(*[ omegas[1+c_i[iDim]] for iDim in range(0,d) ]) / pi**(d/2), c)) |