An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations
Abstract
In this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integration method for the shallow water equations. Due to the positivity-preserving property of mPDeC, the resulting scheme is unconditionally positivity preserving for the water height. To apply the mPDeC approach, we have to interpret the spatial semi-discretization in terms of production-destruction systems. Only small modifications inside the classical WENO implementation are necessary and we explain how it can be done. In numerical simulations, focusing on a fifth order method, we demonstrate the good performance of the new method and verify the theoretical properties.
Keywords
Cite
@article{arxiv.2110.13509,
title = {An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations},
author = {Mirco Ciallella and Lorenzo Micalizzi and Philipp Öffner and Davide Torlo},
journal= {arXiv preprint arXiv:2110.13509},
year = {2022}
}