Reliability of first order numerical schemes for solving shallow water system over abrupt topography
For researchers using numerical schemes for shallow water flows over abrupt topography, this paper highlights resolution-dependent reliability issues and proposes a fix for a known technique.
The paper compares first-order well-balanced numerical schemes for shallow water systems over abrupt topography, showing that required space step for a given error varies by method and that insufficient resolution can yield significantly different solutions. A modification to the hydrostatic reconstruction technique is proposed to avoid neglecting large bottom discontinuities.
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.