Predictor–corrector scheme for the solution of shallow water equations

Abstract

In this paper we consider an explicit difference predictor–corrector scheme of the second order of approximation for solving one-dimensional nonlinear shallow water equations, which yields nonoscillating profiles of discontinuous solutions with the proposed choice of the approximation viscosity of the scheme. For linearized shallow water equations the proposed scheme retains the Riemann invariants monotonicity. The choice of approximation viscosity is based on the study of the dispersion of the differential approximation of the scheme for a one-dimensional scalar equation. We give the generalization of the scheme to the case of movable grids. The proposed scheme has properties similar to those of the known TVD schemes with minmod-type limiters [3].