Xingwang Chen, Old Dominion University


A Comparative Study of the Lattice Boltzmann Models

Abstract: There are four formulations of the lattice Boltzmann equation (LBE) which are applied to simulate the incompressible Navier-Stokes equation, including the multiple relaxation time (MRT) model [1, 2], two relaxation time (TRT) model [3], the lattice BGK (LBGK) equation [4-6], and the entropic lattice Boltzmann equation (ELBE) [7]. These LBE models have been proposed for some time, however, there is no comprehensive and definitive comparison of these models in the literature. In this study, we conduct a comparative study the aforementioned LBE models in terms of accuracy, stability, and efficiency. We compare the ELBE, LBGK, TRT, and MRT LBE models by using the incompressible flow in the lid-driven cavity floow in two-dimensions with the standard bounce-back conditions as a test case. We quantitative compute the following quantities: (1) the precise position of boundary location of a wall, (2) the minimum grid Reynold number can be used with fixed viscosity and grid size but varying lid velocity; and (3) the number of iterations needed to reach a steady state with a fixed Reynolds number and grid size. Our comparison shows that the MRT-LBE is superior in terms of accuracy, stability, and efficiency. The TRT-LBE is accurate but does not address the stability issue. The LBGK and ELBE are similar in terms of accuracy and stability. We note that the ELBE does not improve the stability of the LBGK model, and it is must less efficient than LBGK model.

Collaborator and Mentor: Li-Shi Luo (Old Dominion University)

References:

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