Well-balanced roe-type scheme for 2D shallow water flow using unstructured grids

In order to establish the balance between the bed slope source terms and the gravity gradient terms,a method to treat the bed slope source terms considering different components of the bed slope term separately is proposed in this paper.The paper develops a numerical model for solving two dimensional shallow water flow equation with complicated topography over unstructured grids.The Roe′s approximate Riemann solver is used in the calculation of interface flux.The implicit method is used to calculate the friction source terms and enhance the stability of calculation.It is confirmed by an algebraic manipulation that the proposed scheme is well balanced.The good quality of the results is illustrated by means of two examples.