Numerical Simulation of High Mach Number Flow using the Finite Difference Lattice Boltzmann Method (FDLBM)

Seyedabbas Sadatsakak

doi:10.17485/ijst/2016/v9i32/97590

Abstract

The Lattice Boltzmann Method (LBM) is known as a powerful numerical tool to simulate fluid flow problems. Particularly, it has shown a unified strength for solving incompressible fluid flows in complicated geometries. Many researchers have used Lattice Boltzmann (LB) concept to simulate compressible flows, but the common defect of most of previous models is the stability problem at high Mach number fluid flows. In this paper we introduce a FLDBM-model, which is capable to simulate fluid flows with any specific heat ratios and higher Mach numbers, from 0 to 30 or higher. Compressibility is applied using multiple particle speeds in a thermal fluid. Based on the discrete-velocity-model, a new finite difference method and an artificial viscosity are implemented, which must find a balance between numerical stability and accuracy of simulation. The introduced model is checked and validated again well-known benchmark tests such as one dimensional shock tubes, supersonic bump and ramp (two dimensional). Both sets of results have a reasonable agreement regarding to exact solutions.

Highlights

In the past two decades the lattice Boltzmann (LB) method got rapid development and has been successfully applied in simulating many physical phenomena in various complex systems, especially in simulating incompressible fluids [1]
The FDLBM can secure the numerical stability by selecting an appropriate time increment
In this paper we approach the non-isothermal gas flow using the general description of finite-difference lattice Boltzmann (FDLB) thermal model with multiple speeds of Watari and Tsutahara [15], which allows the correct recovery of mass, momentum and energy equations of a compressible fluid

Summary

Introduction

In the past two decades the lattice Boltzmann (LB) method got rapid development and has been successfully applied in simulating many physical phenomena in various complex systems, especially in simulating incompressible fluids [1]. Having long been attempted, the application of LB to high-speed compressible flows still needs substantial effort. The current lattice Boltzmann method still has a few undesirable shortcomings that limit its general application as a practical computational fluid dynamics tool. One of these shortcomings is the low Mach number constraint. Having achieved great success in simulating incompressible fluids, the application of LB to high-speed compressible flows still needs substantial effort. The FDLBM can secure the numerical stability by selecting an appropriate time increment

Finite difference lattice Boltzmann method with Flexible Specific Heat Ratio

Modified Lax–Wendroff Scheme and Artificial Viscosity

Numerical tests and analysis

Conclusions