High-order Accurate Spectral Difference Method for Shallow Water Equations

ABSTRACT The conservative high-order accurate spectral difference method is presented for simulation of rotating shallowwater equations. The method is formulated using Lagrange interpolations on Gauss-Lobatto points for the desired order of accuracy without suffering numerical dissipation and dispersion errors. The optimal third-order total variation diminishing (TVD) Runge-Kutta algorithm is used for the time marching process. The Godunov-type method by solving the Riemann problem approximately using Roe's technique is utilized at the element interfaces to couple the discontinuous element together at that point. Some 1D and 2D shallow water wave propagation problems with Gaussian shaped water drops are simulated and compared for different order constrictions of spectral difference method. The results from the second-order central difference scheme and the Lax-Wendroff scheme are also included for comparison purposes. The results show that spectral difference method is a good numerical tool for accurate simulation of shallow water equations without suffering the dispersive or dissipative errors and provides an alternative to other high-order accuracy methods in terms of efficiency.