Topical Problems of Fluid Mechanics


Institute of Thermomechanics AS CR, v.v.i.	CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics	MIO Université du Sud Toulon Var - AMU - CNRS - IRD	Czech Pilot centre ERCOFTAC

Runge-Kutta Discontinuous Galerkin Method Applied to Shallow Water Equations with Flooding and Drying Treatment
Poussel C., Ersoy M., Golay F.
Abstract:
This work is devoted to the numerical simulation of Shallow Water Equations involving dry areas and a moving shoreline. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Problems with dry areas are challenging problems for such methods. To counter this issue, special treatment is applied around the shoreline. This work compares two treatments, one based on slope modification and one based on p-adaptation.
Keywords:
Discontinuous Galerkin method, Shallow Water Equations, Flooding and drying, positivity preserving.

Fulltext: PDF DOI: https://doi.org/10.14311/TPFM.2024.022

In Proceedings Topical Problems of Fluid Mechanics 2024, Prague, 2024, Edited by David Šimurda and Tomáš Bodnár, pp. 166 ISBN 978-80-87012-88-8 (Print) ISSN 2336-5781 (Print)