Study on the numerical solution methods for shallow water equations

According to the basic idea of pressure correction algorithm for the Navier-Stokes equations,the water level correction algorithm for the shallow water equations is proposed in the paper,which can greatly reduce restrictions on time step.By reconstructing the coefficient matrix of the original algebraic system,a high-resolution finite element scheme based on unstructured grids is established,so that both the requirement of high-order of accuracy and non-oscillatory condition are satisfied.For the sake of convergence or fasting convergence,the friction terms of the momentum equations are transposed and linearized.Comparisons with analytical solutions are made and good agreements are obtained.