Prandtl number effects in MRT Lattice Boltzmann models for shocked and unshocked compressible fluids

TL;DR

This paper introduces a new MRT Lattice Boltzmann model capable of simulating both shocked and unshocked compressible fluids, with a focus on the effects of Prandtl number variations, validated through benchmark tests.

Contribution

A novel MRT Lattice Boltzmann model that accurately handles both shocked and unshocked compressible fluids by modifying collision operators for energy flux.

Findings

Model accurately simulates thermal Couette flow, Riemann problem, and Richtmyer-Meshkov instability.

Prandtl number effects are effectively captured and validated against analytical and numerical results.

The model shows satisfying agreement with established benchmarks across different flow regimes.

Abstract

For compressible fluids under shock wave reaction, we have proposed two Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) models [F. Chen, et al, EPL \textbf{90} (2010) 54003; Phys. Lett. A \textbf{375} (2011) 2129.]. In this paper, we construct a new MRT Lattice Boltzmann model which is not only for the shocked compressible fluids, but also for the unshocked compressible fluids. To make the model work for unshocked compressible fluids, a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system. The unnecessity of the modification for systems under strong shock is analyzed. The model is validated by some well-known benchmark tests, including (i) thermal Couette flow, (ii) Riemann problem, (iii) Richtmyer-Meshkov instability. The first system is unshocked and the latter two are shocked. In all the three systems, the Prandtl numbers effects are checked. Satisfying agreements are obtained between new model results and analytical ones or other numerical results.