Study on semi-discrete central-upwind scheme for the 2-D shallow water equations

Based on the third-order central weighted essentially non-oscillatory(CWENO) reconstruction,a high-resolution semi-discrete central-upwind difference scheme for solving the 2-D shallow water equations is presented by using the dimension-by-dimension approach.The reconstruction is chosen to improve the accuracy and guarantee the non oscillatory behavior of the present scheme.The optimal third-order SSP(Strong Stability Preserving) Runge-Kutta method is used for time discrete Since no Riemann solvers are required and characteristic decomposition can be avoided,the resulting scheme retains all the advantages of central scheme.For the numerical treatment of source terms,the Simpson’s quadrature rule is used.The simulated results are shown to be in good agreement with numerical results obtained by other methods These results demonstrate that the present method is efficient and stable.