Initialization of lattice Boltzmann models with the help of the numerical Chapman-Enskog expansion

TL;DR

This paper extends the numerical Chapman-Enskog expansion to serve as a lifting operator for lattice Boltzmann models, enabling the initialization of distribution functions from density and momentum data.

Contribution

It introduces an extended method for initializing lattice Boltzmann models using the numerical Chapman-Enskog expansion to map macroscopic variables to distribution functions.

Findings

Effective initialization of lattice Boltzmann models from density and momentum.

Improved accuracy in the mapping process.

Extension of previous methods to include velocity moments.

Abstract

We extend the applicability of the numerical Chapman-Enskog expansion as a lifting operator for lattice Boltzmann models to map density and momentum to distribution functions. In earlier work [Vanderhoydonc et al. Multiscale Model. Simul. 10(3): 766-791, 2012] such an expansion was constructed in the context of lifting only the zeroth order velocity moment, namely the density. A lifting operator is necessary to convert information from the macroscopic to the mesoscopic scale. This operator is used for the initialization of lattice Boltzmann models. Given only density and momentum, the goal is to initialize the distribution functions of lattice Boltzmann models. For this initialization, the numerical Chapman-Enskog expansion is used in this paper.