Hybrid finite volume WENO and lattice Boltzmann method for shallow flows over erodible bed

Abstract

A hybrid mesh-particle method is developed to simulate hydro- and morpho-dynamics in shallow flows. The well-balanced finite volume WENO and lattice Boltzmann methods were implemented to solve nonlinear shallow water and Exner equations, respectively and a splitting strategy coupled those two solvers. This strategy was known to suffer from numerical instability due to loss of hyperbolicity, but this problem was not observed in the present method. To achieve advanced interaction between two solvers, cross-computation and information exchange were performed at every step of the high-order Runge-Kutta method. Extensive numerical experiments verified whether the present hybrid method was implemented correctly, and the proposed method provided satisfactory results of the well-balanced property, the accuracy, and the stability in verification examples.