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