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

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