Discrete Boltzmann trans-scale modeling of high-speed compressible flows

TL;DR

This paper introduces a versatile discrete Boltzmann modeling framework for high-speed compressible flows, capable of spanning continuum to transition regimes by incorporating higher-order kinetic moments and TNE effects.

Contribution

It develops a trans-scale DBM framework with novel measures for TNE effects, enabling adaptive modeling levels based on TNE intensity rather than Knudsen number.

Findings

Formulated a 2D DBM with 26 velocities at Burnett level

Verified and validated the model against theoretical and experimental data

Provided criteria for selecting appropriate DBM levels based on TNE measures

Abstract

We present a general framework for constructing trans-scale \emph{discrete Boltzmann models} (DBMs) for high-speed compressible flows ranging from continuum to transition regime. This is achieved by designing a higher-order discrete equilibrium distribution function which satisfies additional nonhydrodynamic kinetic moments. In order to characterize the \emph{% thermodynamic non-equilibrium} (TNE) effects and estimate the condition under which the DBMs at various levels should be used, two novel measures are presented: (i) the relative TNE strength, describing the relative strength of the ($N+1$)-th order TNE effects to the $N$-th order one; (ii) the TNE discrepancy between DBM simulation and relevant theoretical analysis. Whether or not the higher-order TNE effects should be taken into account in the modeling and which level of DBM should be adopted, is best described by the relative TNE intensity and/or the discrepancy, rather than by the value of the Knudsen number. As a model example, a two-dimensional DBM with $26$ discrete velocities at Burnett level is formulated, verified, and validated.