Finite volume formulation of thermal lattice Boltzmann method

Abstract

Purpose

The main purpose of this paper is to develop a novel thermal lattice Boltzmann method (LBM) based on finite volume (FV) formulation. Validation of the suggested formulation is performed by simulating plane Poiseuille, backward-facing step and flow over circular cylinder.

Design/methodology/approach

For this purpose, a cell-centered scheme is used to discretize the convection operator and the double distribution function model is applied to describe the temperature field. To enhance stability, weighting factors are defined as flux correctors on a D2Q9 lattice.

Findings

The introduction of pressure-temperature-dependent flux-control coefficients in the streaming operator, in conjunction with suitable boundary conditions, is shown to result in enhanced numerical stability of the scheme. In all cases, excellent agreement with the existing literature is found and shows that the presented method is a promising scheme in simulating thermo-hydrodynamic phenomena.

Originality/value

A stable and accurate FV formulation of the thermal DDF-LBM is presented.

Citation

Zarghami, A., Ubertini, S. and Succi, S. (2014), "Finite volume formulation of thermal lattice Boltzmann method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 2, pp. 270-289. https://doi.org/10.1108/HFF-11-2011-0234