A numerical study of the MRT-LBM for the shallow water equation in high Reynolds number flows: An application to real-world tsunami simulation

Abstract

The lattice Boltzmann method (LBM) has recently attracted attention as a simple computational fluid dynamics (CFD) method that does not directly solve macroscopic equations. Due to the advantage of its local scheme, the LBM is expected to efficiently achieve highly accurate and high-resolution fluid simulations. In particular, the application of the LBM to disaster simulations has been studied since the proposal of the LBM for nonlinear shallow water equations (LABSWE). However, it is well known that the LBM is prone to computational instability in high Reynolds number flows. A tsunami inundating an urban area is considered a high Reynolds number flow because of its violent flow. The numerical stability in such flows must be enhanced for the application of the LBM to real-world tsunami simulations. For this purpose, it is practical to introduce the subgrid-scale (SGS) model into the multiple-relaxation-time (MRT) model. Notably, the MRT model is computationally more expensive than the conventional lattice Bhatnagar–Gross–Krook (BGK) model. In this study, we modified the SGS model for the MRT model. We verified the calculation accuracy by focusing on grid size differences in the classical benchmark problems in high Reynolds number flows. Finally, we simulated the 2011 tsunami off the Pacific coast caused by the Tohoku earthquake. The LBM simulations reproduced the tsunami propagation waveform and inundation depth with the computational accuracy equally as good as that of the finite difference method (FDM).