Multi-dimensional semi-lagrangian characteristic approach to the shallow water equations by the CIP method

We propose a multi-dimensional scheme to solve the shallow water equations by using the CIP(Constrained Interpolation Profile/Cubic Interpolated Pseudoparticle) method which has the accuracy by one-order of magnitude better than the cubic Lagrange. This third-order accuracy is kept even in non-uniform grid, while the cubic Lagrange becomes the first order. The semi-Lagrangian approach to the characteristic equations has been used for solving gravity waves because it can make time step be much longer than the Courant-Friedrichs-Lewy (CFL) condition. Even in two dimensions, the method can give a symmetrical wave propagation under the large CFL condition.