Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium

TL;DR

This paper develops three-dimensional discrete Boltzmann models for simulating compressible flows, including highly non-equilibrium conditions, by constructing equilibrium distribution functions that satisfy kinetic moment relations aligned with non-equilibrium statistical mechanics.

Contribution

The paper introduces a novel scheme for constructing discrete equilibrium distribution functions for 3D Boltzmann models, validated across various benchmarks and capable of handling high Mach and pressure ratios.

Findings

Models accurately reproduce Riemann solutions at high Mach numbers.

Validated models work for flows with large temperature and pressure ratios.

Simulation results show excellent agreement with theoretical solutions.

Abstract

We present a series of three-dimensional discrete Boltzmann (DB) models for compressible flows in and out of equilibrium. The key formulating technique is the construction of discrete equilibrium distribution function through inversely solving the kinetic moment relations that it satisfies. The crucial physical requirement is that all the used kinetic moment relations must be consistent with the non-equilibrium statistical mechanics. The necessity of such a kinetic model is that, with increasing the complexity of flows, the dynamical characterization of non-equilibrium state and the understanding of the constitutive relations need higher order kinetic moments and their evolution. The DB models at the Euler and Navier-Stokes levels proposed by this scheme are validated by several well-known benchmarks, ranging from one-dimension to three-dimension. Particularly, when the local Mach number, temperature ratio, and pressure ratio are as large as $10^2$, $10^4$, and $10^5$, respectively, the simulation results are still in excellent agreement with the Riemann solutions. How to model deeper thermodynamic non-equilibrium flows by DB is indicated. Via the DB method, it convenient to simulate nonequilibrium flows without knowing exact form of the hydrodynamic equations.