Volumetric formulation of lattice Boltzmann models with energy conservation

TL;DR

This paper presents a volumetric lattice Boltzmann method for simulating compressible thermal fluids that conserves energy and other quantities, with flexibility in velocity set design and boundary conditions.

Contribution

It introduces a volumetric formulation that ensures energy conservation without strict space-filling velocity sets, improving simulation accuracy for thermohydrodynamics.

Findings

The method accurately conserves density, momentum, and energy.

It effectively handles boundary conditions and benefits from grid refinement.

Validated against controlled fluid flow problems.

Abstract

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.