Implicit-Explicit Finite-Difference Lattice Boltzmann Model with Varying Adiabatic Index

TL;DR

This paper introduces an implicit-explicit finite-difference lattice Boltzmann model that efficiently simulates perfect fluids with variable adiabatic indices, validated through shock wave propagation tests.

Contribution

It develops a novel IMEX lattice Boltzmann scheme with reduced distribution functions allowing for variable adiabatic indices and efficient shock wave simulation.

Findings

Successfully models shock wave propagation in 1D and 2D

Achieves computational efficiency with reduced distribution functions

Enables simulation of fluids with varying adiabatic indices

Abstract

The perfect fluid limit can be obtained from the Boltzmann equation in the limit of vanishing Knudsen number. By treating the collision term in an implicit manner, the implicit-explicit (IMEX) time stepping scheme allows this limit to be achieved at finite values of the time step. We consider the 9th order monotonicity-preserving (MP-9) scheme to implement the advection, which is treated explicitly in the IMEX approach. We reduce the computational costs using reduced distribution functions, which also permits the adiabatic index to be varied. We validate the capabilities of our model by considering the propagation of shock waves in one-dimensional and two-dimensional setups.