Two dimensional MRT LB model for compressible and incompressible flows

TL;DR

This paper extends a 2D MRT Lattice Boltzmann model to handle both compressible and incompressible flows, using flux limiter schemes to reduce oscillations and validating with benchmark tests.

Contribution

The paper introduces a modified MRT LB model suitable for incompressible flows, enhancing stability and accuracy over previous models.

Findings

Successful validation with Riemann and Couette flow benchmarks.

Reduced artificial oscillations using flux limiter discretization.

Consistent non-equilibrium characteristics with physical analysis.

Abstract

In the paper we extend the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. \textbf{90}, 54003 (2010)] so that it is suitable also for incompressible flows. To decrease the artificial oscillations, the convection term is discretized by the flux limiter scheme with splitting technique. New model is validated by some well-known benchmark tests, including Riemann problem and Couette flow, and satisfying agreements are obtained between the simulation results and analytical ones. In order to show the merit of LB model over traditional methods, the non-equilibrium characteristics of system are solved. The simulation results are consistent with physical analysis.