A well-balanced reconstruction for wetting/drying fronts
Numerical Analysis
2014-12-12 v1
Abstract
In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet-dry cells, which is presented in this paper for the one dimensional case. We realize the new reconstruction in the framework of the second-order semi-discrete central-upwind scheme from (A. Kurganov and G. Petrova, Commun. Math. Sci., 2007). The positivity of the computed water height is ensured following (A. Bollermann, S. Noelle and M. Luk\'a\v{c}ov\'a-Medvi\v{d}ov\'a, Commun. Comput. Phys., 2010): The outgoing fluxes are limited in case of draining cells.
Keywords
Cite
@article{arxiv.1412.3580,
title = {A well-balanced reconstruction for wetting/drying fronts},
author = {Andreas Bollermann and Guoxian Chen and Alexander Kurganov and Sebastian Noelle},
journal= {arXiv preprint arXiv:1412.3580},
year = {2014}
}