Abstract
In this paper, we propose a numerical simulation of two-phase shallow granular flows through a moved bed with a variable irregular topography via a predictor corrector scheme. This method consists of predictor and corrector stages. The predictor stage contains a parameter to control the numerical diffusion that is performed by utilizing limiters and Riemann invariant theory. The corrector stage recovers the balance conservation equation. In the first part, we solve numerically the one-dimensional equation for two-phase shallow granular flows over a fixed bed with irregular topography. In the second part, we consider the model equations for the bed-load sediment transport, the governing model equations consist of two components, specifically, a geophysical flows part and interstitial fluid. The sediment part is described by the Exner equation when the velocity can be considered to be the solid velocity, fluid velocity or a mean value of both of them.(c) 2022 Elsevier Masson SAS. All rights reserved.