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Spectral Closure for the Linear Boltzmann-BGK Equation

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arxiv 2306.07103 v1 pith:APLNN526 submitted 2023-06-12 math.AP math-phmath.MP

Florian Kogelbauer , Ilya Karlin This is my paper · ORCID
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keywords spectralboltzmann-bgklinearclosuredynamicsequationequationsfluid
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We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model which is valid for any relaxation time. The non-local exact fluid dynamics equations are compared to the Euler, Navier--Stokes and Burnett equations. Our results are based on a detailed spectral analysis of the linearized Boltzmann-BGK operator together with a suitable choice of spectral projection.

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  1. Learning the Optimal Hydrodynamic Closure

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    A neural network trained on density fluctuations learns generalized transport coefficients that reproduce Shakhov and DSMC spectra up to Knudsen number 10, extending spectral closure hydrodynamics beyond its critical ...

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