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-rw-r--r--boltzgen/lbm/model/characteristics.py27
1 files changed, 0 insertions, 27 deletions
diff --git a/boltzgen/lbm/model/characteristics.py b/boltzgen/lbm/model/characteristics.py
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--- a/boltzgen/lbm/model/characteristics.py
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-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))
-
-# determine lattice speed of sound using directions and their weights
-def c_s(d, c, w):
- speeds = set([ sqrt(sum([ w[i] * c_i[j]**2 for i, c_i in enumerate(c) ])) for j in range(0,d) ])
- assert len(speeds) == 1 # verify isotropy
- return speeds.pop()