Finite volume model for the 2D shallow water equations using modified Roe scheme

A numerical model for finite volume method is developed for two-dimensional shallow-water flow with complicated geometry and topography.Based on the unstructured grid,the Roe′s approximate Riemann solver is used for the computation of inviscid numerical flux functions.The bed slope source terms are computed by three vertices bottom value of a triangle lie on the same plane.Therefore,the discrete accuracy of landform is guaranteed.In order to balance the pressure terms with the bed slope source term for arbitrary geometry with triangular mesh,the classical Roe scheme is improved.The improved Roe scheme is confirmed to be well balanced by algebraic manipulation.The validity of the proposed modeling method is verified by the oblique shock wave and the transcritical flow with a shock numerical example.