On lattice Boltzmann scheme, finite volumes and boundary conditions

TL;DR

This paper establishes a natural connection between Boltzmann schemes and finite volume methods, deriving flux expressions and demonstrating high accuracy in boundary condition treatments for fluid simulations.

Contribution

It introduces a novel framework linking Boltzmann schemes with finite volume methods, focusing on flux boundary conditions and validating accuracy through test cases.

Findings

High accuracy achieved with the proposed scheme

Effective treatment of flux boundary conditions

Potential for improved fluid simulation methods

Abstract

We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann scheme induces general expressions for mass and momentum fluxes. We treat a unidimensional case and focus our development in two dimensions on possible flux boundary conditions. Several test cases show that a high level of accuracy can be achieved with this scheme.