Comparative study of discrete Boltzmann model and Navier-Stokes

TL;DR

This paper compares the discrete Boltzmann model and Navier-Stokes model in simulating fluid flows, highlighting their respective advantages in accuracy and computational efficiency depending on the strength of thermodynamic non-equilibrium effects.

Contribution

It provides a systematic comparison of DBM and NS models in flow simulations, emphasizing their physical capabilities and computational costs.

Findings

DBM offers detailed non-equilibrium information.

NS is more efficient for weak TNE effects.

Both models are accurate for hydrodynamic behavior when TNE effects are weak.

Abstract

Discrete Boltzmann model (DBM) is a type of coarse-grained mesoscale kinetic model derived from the Boltzmann equation. Physically, it is roughly equivalent to a hydrodynamic model supplemented by a coarse-grained model for the relevant thermodynamic non-equilibrium (TNE) behaviours. The Navier-Stokes (NS) model is a traditional macroscopic hydrodynamic model based on continuity hypothesis and conservation laws. In this study, the two models are compared from two aspects, physical capability and computational cost, by simulating two kinds of flow problems including the thermal Couette flow and a Mach 3 step problem. In the cases where the TNE effects are weak, both the two models give accurate results for the hydrodynamic behaviour. Besides, DBM can provide more detailed non-equilibrium information, while the NS is more efficient if concern only the density, momentum, energy and their derived quantities. It is concluded that, if the TNE effects are strong or are to be investigated, the NS is insufficient while DBM is a good choice. While in the cases where the TNE effects are weak and only the macro flow fields are to be studied, the NS is more preferable.