A comparison of lattice Boltzmann schemes for sub-critical shallow water flows

Abstract

In this paper, we test the numerical properties of several variants of the lattice Boltzmann method (LBM) for simulating the shallow water flows. Specifically, we perform a systematic comparison of five different schemes: (i) the single-relaxation-time LBM, the (ii) raw-moments-based and (iii) central-moments-based multiple-relaxation-time LBMs, and the (iv) two-stages and (v) one-stage simplified LBMs. Concerning the latter, traditional simplified schemes require a fractional step two-stages technique. Building on the work Delgado-Gutiérrez et al. [“A single-step and simplified graphics processing unit lattice Boltzmann method for high turbulent flows,” Int. J. Numer. Methods Fluids 93, 2339–2361 (2021)], we derive a one-stage approach, where the procedure spans the grid points just once per time step. All the aforementioned LBMs are tested against five well-consolidated benchmark problems, and their numerical performance is assessed. Overall, populations-based schemes show superior accuracy and convergence properties. We link this behavior to the higher numerical dissipation introduced by the simplified models.