Application of Surface Gradient Method in Flux-Vector Splitting for Numerical Solution of Shallow Water Equations

Abstract

This paper presents the solution of shallow water equations using the flux-difference splitting method. To handle more complex geometries, the governing equations are transferred from the physical to the computational domain by using boundary-fitted curvilinear coordinates. Roe's method has been employed to evaluate the numerical flux and the finite-volume approach has been used to discretize the equations. To ensure the balance of source term and flux gradient, the simple and powerful Surface Gradient Method (SGM) has been adopted, which not only enables the model to simulate flow over uneven bed topography but makes it shock-capturing as well. Some classical problems have been modeled to show that the results obtained from the proposed model are in good agreement with those of analytical solutions and other numerical methods.

Keywords

• Flux-Difference Splitting
• Two-Dimensional Open Channel Flow
• High- Resolution Scheme