An efficient shock capturing scheme for two-dimensional, open channel, unsteady flows in a generalised coordinate system

An efficient algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a nonrectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalised coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme is efficient, has good jump capturing properties and the advantage of using boundary/body-fitted meshes.