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
Poussel C., Ersoy M., Golay F., Mannes Y.
Abstract:
This work is devoted to the numerical simulation of Shallow Water Equations using Runge-Kutta Discontinuous Galerkin methods. Such methods were implemented in the framework of adaptive mesh refinement method using a block-based approach. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Increasing the order of approximation, spurious oscillations appear and are addressed using moment limiters. Finally, the solver is validated with a one-dimensional dam-break problem and its behavior is tested solving a two-dimensional benchmark.
Keywords:
Discontinuous Galerkin method, Shallow Water Equations, Moment limiter, Nonconformal mesh

Fulltext: PDF DOI: https://doi.org/10.14311/TPFM.2023.021

In Proceedings Topical Problems of Fluid Mechanics 2023, Prague, 2023, Edited by David Šimurda and Tomáš Bodnár, pp. 152 ISBN 978-80-87012-83-3 (Print) ISSN 2336-5781 (Print)