Comparative study of discrete Boltzmann model and Navier-Stokes

Yudong Zhang,Guangcai Zhang,Aiguo Xu

doi:10.1088/1742-6596/1113/1/012015

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.

Highlights

In recent years, discrete Boltzmann model (DBM) has been well developed to investigate various of complex flow situations where the thermodynamic non-equilibrium effect (TNE) is significant [1, 2, 3]
The evolution equations of DBM are a set of the discrete particle velocity distribution, while the evolution equations of NS are those for the conservation laws of mass, momentum, and energy of control volume
Thermal Couette flow Firstly, the thermal Couette flow is simulated by using DBM and numerical solving NS equations

Summary

Introduction

Discrete Boltzmann model (DBM) has been well developed to investigate various of complex flow situations where the thermodynamic non-equilibrium effect (TNE) is significant [1, 2, 3]. 1. Introduction In recent years, discrete Boltzmann model (DBM) has been well developed to investigate various of complex flow situations where the thermodynamic non-equilibrium effect (TNE) is significant [1, 2, 3]. It provides a new point of view to study the non-equilibrium characteristics of flow system. Compared with traditional hydrodynamic model, the Navier-Stokes (NS) equation [13, 14], DBM has more kinetic information.

Results

Conclusion