Reliability of first order numerical schemes for solving shallow water system over abrupt topography

Abstract

We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed error depends on the method. Moreover, the solutions given by the numerical scheme can be significantly different if not enough space resolution is used. We shall pay special attention to the well-known hydrostatic reconstruction technique where it is shown that large bottom discontinuities may be neglected and a modification is proposed to avoid this problem.

References in corpus (2)

• Why many theories of shock waves are necessary. Convergence error in formally path-consistent schemes
• A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime

Cited by in corpus (5)

• Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models
• Invariant conservative difference schemes for shallow water equations in Eulerian and Lagrangian coordinates
• A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes
• A fully well-balanced hydrodynamic reconstruction
• Entropy stable flux correction for hydrostatic reconstruction scheme for shallow water flows