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arXiv · 1510.08224

Non-orthogonal multiple-relaxation-time lattice Boltzmann method for incompressible thermal flows

Qing Liu·Ya-Ling He·Dong Li·Qing Li
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Abstract

In this paper, a non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method for simulating incompressible thermal flows is presented. In the method, the incompressible Navier-Stokes equations and temperature equation are solved separately by two different MRT-LB equations, which are developed based on non-orthogonal basis vectors obtained from the combinations of the lattice velocity components. The macroscopic governing equations of incompressible thermal flows can be recovered from the method through the Chapman-Enskog analysis in the incompressible limit. Numerical simulations of several typical two-dimensional problems are carried out to validate the proposed method. It is found that the present results are in good agreement with the analytical solutions and/or other numerical results reported in the literature. Furthermore, the non-orthogonal MRT-LB model shows better numerical stability in comparison with the BGK-LB model, and the grid convergence tests indicate that the present MRT-LB method has a second-order convergence rate in space.

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Qing Liu, Ya-Ling He, Dong Li, Qing Li. 2016-07-07. Non-orthogonal multiple-relaxation-time lattice Boltzmann method for incompressible thermal flows. https://arxiv.org/abs/1510.08224

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