Spectral Closure for the Linear Boltzmann-BGK Equation

TL;DR

This paper derives a new linear fluid dynamics model from the linear Boltzmann-BGK equation using spectral analysis, valid for any relaxation time, and compares it to classical fluid equations.

Contribution

It provides an explicit spectral closure for the linear Boltzmann-BGK equation, leading to a novel fluid model applicable across all relaxation times.

Findings

Derived a spectral closure explicitly in terms of macroscopic fields.

Compared the new fluid model to Euler, Navier-Stokes, and Burnett equations.

Validated the model through spectral analysis of the linearized operator.

Abstract

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.