Stochastic cellular automaton

Quantum mechanics

Compressibility

Algorithm

Turbulence

Discretization

Reynolds number

Applied mathematics

Computer science

Statistical physics

Geology

Physics

Boltzmann equation

Mathematics

Cellular automaton

Compressible flow

Inviscid flow

Numerical stability

HPP model

Mathematical analysis

Numerical analysis

Mechanics

Lattice Boltzmann methods

Lattice gas automaton

Numerical Heat Transfer Part A Applications

In this article, we propose a numerical framework based on multiple relaxation time lattice Boltzmann (LB) model and novel discretization techniques for simulating compressible flows. Highly efficient finite difference lattice Boltzmann methods are employed to simulate one- and two-dimensional compressible flows. These numerical techniques are applied on the single- and multiple-relaxation-time on the 16-discrete-velocity (Kataoka and Tsutahara, Phys. Rev. E, 69(5):056702, 2004) compressible lattice Boltzmann model. The Boltzmann equation is discretized via modified Lax-Wendroff and modified total variation diminishing schemes which have ability to damps oscillations at discontinuities, effectively. The results of compressible models are compared and validated with the well-known inviscid compressible flow benchmark test cases, so called Riemann problems. The proposed method shows its superiority over available techniques when compared to the analytical solutions. It is then used to solve two-dimensional inviscid compressible flow benchmarks, including regular shock reflection and Richtmyer–Meshkov instability problems to ensure its applicability for more complex problems. It is found that, the applied discretization techniques improve the stability of original LB models and enhance the robustness of compressible flow problems by preventing the formation of oscillation.

Numerical simulation of compressible flows by lattice Boltzmann method