Probing double distribution function models in the lattice Boltzmann method for highly compressible flows

TL;DR

This paper evaluates various double distribution function models in the lattice Boltzmann method for simulating highly compressible flows, comparing their accuracy, computational cost, and hydrodynamic consistency.

Contribution

It provides a comprehensive overview and comparative analysis of energy partition strategies in lattice Boltzmann models for compressible flows, highlighting the total energy split as optimal.

Findings

Total energy split offers the best overall performance.

Non-translational energy split requires higher-order quadrature.

Internal energy split involves higher computational cost and memory overhead.

Abstract

The double distribution function approach is an efficient route towards extension of kinetic solvers to compressible flows. With a number of realizations available, an overview and comparative study in the context of high speed compressible flows is presented. We discuss the different variants of the energy partition, analyses of hydrodynamic limits and a numerical study of accuracy and performance with the particles on demand realization. Out of three considered energy partition strategies, it is shown that the non-translational energy split requires a higher-order quadrature for proper recovery of the Navier--Stokes--Fourier equations. The internal energy split on the other hand, while recovering the correct hydrodynamic limit with fourth-order quadrature, comes with a non-local --both in space and time-- source term which contributes to higher computational cost and memory overhead. Based on our analysis, the total energy split demonstrates the optimal overall performance.