Open Access

ARTICLE

Assessment and Computational Improvement of Thermal Lattice Boltzmann Models Based Benchmark Computations

R. Djebali¹, M. El Ganaoui²

1 Univ. of Tunis el Manar, FST/LETTM, Tunis 2092, Tunisia. jbelii_r@hotmail.fr
2 Univ. of Limoges, SPCTS/CEC, 87068 Limoges, France.

Computer Modeling in Engineering & Sciences 2011, 71(3), 179-202. https://doi.org/10.3970/cmes.2011.071.179

Abstract

The Lattice Boltzmann method (LBM) became, today, a powerful tool for simulating fluid flows. Its improvements for different applications and configurations offers more flexibility and results in several schemes such as in presence of external/internal forcing term. However, we look for the suitable model that gives correct informations, matches the hydrodynamic equations and preserves some features like coding easily, preserving computational cost, stability and accuracy. In the present work, high order incompressible models and equilibrium distribution functions for the advection-diffusion equations are analyzed. Boundary conditions, acceleration, stability and preconditioning with initial fields are underlined which permit to rigorously selecting two LBGK thermal models. The two selected models are modified, leading to two new schemes going well with the above mentioned computational advantages. The standard and modified schemes have been validated on benchmark computations based two-dimensional natural convection problems for steady flows. First, the standard and modified schemes are intensively tested on a heated differentially air-filled cavity for a wide range of Rayleigh number. Following, we present the predictability level of a selected model based transitional two test cases concerning process of solidification, since these flows types present transition thresholds in the dynamic behaviour. The produced results are compared to high-order accurate solutions in available literature finding results. It is found that the commonly used LB thermal models give similar and consistent results. However, they are time consuming in its standard forms. The modified models show an improvement of the computational cost and permit to suggest an appropriate model based on the most required features in Computational Fluid Dynamics.

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Keywords

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