Solution of 2D shallow water equations with complicated geometry using modified HLL scheme

A numerical model based on the unstructured grid finite volume method is developed for two-dimensional shallow water equation with complicated geometry.The HLL approximate Riemann solver is used for the computation of numerical flux functions.Based on triangular grid,the bed slope source terms are computed since three vertices of a triangle lie on the same plane.The friction source terms are treated in a fully implicit way to alleviate stabilities of the scheme.To achieve high-order spatial accuracy and prevent nonphysical oscillations,the multidimensional reconstruction technique and multidimensional limiter are employed.The time discretization is made by the third-order Runge-Kutta method to accomplish high-order temporal accuracy.To balance the pressure and bed slope terms,the hydrostatic pressure term in the momentum equation is corrected.The good quality of the results verifies that the scheme has good capability of shock capturing,and can be applied to real flows with complex boundary.