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author | Adrian Kummerlaender | 2019-10-21 18:42:24 +0200 |
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committer | Adrian Kummerlaender | 2019-10-21 18:48:38 +0200 |
commit | 82a44e0d64afb8818ea98d68dc08108885d503c2 (patch) | |
tree | 6e8f08acd83b2886cd296ed3831acc83e309906c /boltzgen/lbm/model/characteristics.py | |
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Pull in basics from symlbm_playground
It's time to extract the generator-part of my GPU LBM playground and turn it
into a nice reusable library. The goal is to produce a framework that can be
used to generate collision and streaming programs from symbolic descriptions.
i.e. it should be possible to select a LB model, the desired boundary
conditions as well as a data structure / streaming model and use this
information to automatically generate matching OpenCL / CUDA / C++
programs.
Diffstat (limited to 'boltzgen/lbm/model/characteristics.py')
-rw-r--r-- | boltzgen/lbm/model/characteristics.py | 27 |
1 files changed, 27 insertions, 0 deletions
diff --git a/boltzgen/lbm/model/characteristics.py b/boltzgen/lbm/model/characteristics.py new file mode 100644 index 0000000..b68afeb --- /dev/null +++ b/boltzgen/lbm/model/characteristics.py @@ -0,0 +1,27 @@ +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() |