A fifth order WENO scheme for numerical simulation of shallow granular two-phase flow model

Abstract

In this article, a weighted essentially non-oscillatory (WENO) scheme is implemented to simulate two-phase shallow granular flow (TPSF) model. The flow is assumed to be incompressible and it is regarded as shallow layer of granular and liquid material. The mathematical model consists of two phases, that is, solid and liquid. Each phase has its continuity and momentum equation. The presence of the equations are coupled together involving the derivatives of unknowns which make it more challenging to solve. An efficient numerical technique is needed to tackle the numerical complexities. Our main intrigue is the numerical approximation of the above-mentioned solid-liquid model. The weighted essentially non-oscillatory (WENO) scheme of order 5 is utilized to handle the shock waves and contact discontinuities appear in the solution. The results are compared with the results already available in the literature by conservation element and solution element (CESE) scheme. It is observed the WENO scheme produces less errors as compared to CESE scheme and also effectively handle the shocks.