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Hou-Li-type exponential Hermite filter skipping n <= 2 (exposed spectrum) - #61
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…ectrum exposed filter_spectrum(Nn, Nm, Np, order, keep=2) gives s(n) = (n/(N-1))**order for n > keep, summed over axes; exponential_filter(Ck, strength, s) applies exp(-strength*s) between steps (zero strength is bitwise identity). Passed as collision_matrix with nu = rate it is the equivalent RHS damping. Moments of total degree <= 2 are untouched for any basis.
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Hou-Li-type exponential Hermite filter that skips n <= 2 (stacked on #60).
What
filter_spectrum(Nn, Nm, Np, order=36, keep=2)returns the exposed shapes(n) = (n/(N-1))**orderforn > keep, and exactly 0 forn <= keep, summed over the velocity axes. Shape(Np, Nm, Nn), likehypercollision_spectrum.exponential_filter(Ck, strength, s)appliesexp(-strength*s)between steps. Hou & Li use strength = order = 36. With zero strength the state is returned unchanged, bitwise.sas"collision_matrix"withnu = rate. Over a time dt this is the filter withstrength = rate*dt, and it needs no driver change.keep = 2, every moment of total degree <= 2 (density, momentum, full pressure tensor) is untouched for any basis centre and width.Tests (local only) in
tests/test_filter.py:-rate*s*Cexactly.Full suite at 7b94668:
python -m pytest -q -n 2 testsgave 191 passed (macOS, Python 3.12, JAX 0.11.2, diffrax 0.7.2). GitHub CI does not run on PRs that do not target main.Dependencies: #56–#60. Merge after #60.
Open question: default order 36 (Hou-Li) vs a gentler order for RHS use. The physics study using it, with strength and order varied, is in Dark-SPECTRAX branch
lane-a.