A central-upwind scheme for two-phase shallow granular flow model

Abstract

In this article, a central-upwind scheme (CUP) is extended to solve two-phase shallow granular flow (TPSF) model. The flow in this case is considered as incompressible and it is regarded to be a shallow layer of granular and liquid material. The model consists of continuity and momentum equations for both solid and liquid phases. Our main intrigue is the numerical approximation of the above-mentioned solid-liquid model, the complexity of which raises numerical challenges. The proposed method is non-oscillating upwind biased that does not require a Riemann solver at each step. A few test problems are approximated numerically to check the performance of suggested scheme. For validation the outcomes are compared with the conservation element solution element (CE/SE) and kinetic flux vector splitting (KFVS) schemes.

Keywords

• Two-phase shallow granular model
• Central-upwind scheme
• CE/SE scheme
• KFVS scheme
• Non-conservative systems