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arXiv · 2012.10678

A multiple-relaxation-time lattice Boltzmann model based four-level finite-difference scheme for one-dimensional diffusion equation

Yuxin Lin·Ning Hong·Baochang Shi·Zhenhua Chai
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Abstract

In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient $\omega_{0}$ and the relaxation parameters $s_1$ and $s_2$ corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations, and find that the numerical results are consistent with our theoretical analysis.

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Yuxin Lin, Ning Hong, Baochang Shi, Zhenhua Chai. 2020-12-19. A multiple-relaxation-time lattice Boltzmann model based four-level finite-difference scheme for one-dimensional diffusion equation. https://doi.org/10.1103/physreve.104.015312

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