Numerical modelling of one dimensional problems for the shallow water equations on an adaptive moving meshes

Abstract

This work is devoted to an approach for the quality improvement of numerical solving of initial-boundary problems for one-dimensional shallow water equations on an adaptive mesh. A Godunov type numerical scheme for the problem on moving mesh is applied. The grid motion law is based on the solution of the local Riemann discontinuity breakdown problem and forces the computational nodes to follow the wave of the greatest amplitude. The regularization mechanism prevents the degeneration of moving computational mesh and gives an estimate for the mesh compression. The proposed algorithm is tested on several typical Riemann problems with known exact solutions. The numerical experiments show that the proposed approach allows to improve the quality of the obtained numerical solution.