A high resolution Gauss scheme with staggered grid for shallow water equation

Based on the high accurate Gauss integral formula,a high resolution and totally two orders accurate scheme is designed by using a staggered grid for shallow water equation.The difference scheme does not face to solve Riemann problem due to use the staggered grid,so the difference scheme has the specialty of simple computing and convenient programming.By the way,in one-dimensional scalar equation,the difference scheme is TVD (Total Variation Diminishing scheme) with CFL (Courant Friedrich Lewy) condition.In two- and three-dimensional cases,the scheme has MmB (Maximum and Minimum Bounds Preserving) property.With the Shuguang-1000 distribution storage vast scale parallel computer at the computing center of China,the high resolution difference scheme for solving shallow water equation with the staggered grid is used to numerical simulate several typical program,the computed results are satisfy.