Riemann Solvers with Runge–Kutta Discontinuous Galerkin Schemes for the 1D Shallow Water Equations
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 2
Abstract
The spectrum of this survey turns on the evaluation of some eminent Riemann solvers (or the so-called solver), for the shallow water equations, when employed with high-order Runge–Kutta discontinuous Galerkin (RKDG) methods. Based on the assumption that: The higher is the accuracy order of a numerical method, the less crucial is the choice of Riemann solver; actual literature rather use the Lax-Friedrich solver as it is easy and less costly, whereas many others could be also applied such as the Godunov, Roe, Osher, HLL, HLLC, and HLLE. In practical applications, the flow can be dominated by geometry, and friction effects have to be taken into consideration. With the intention of obtaining a suitable choice of the Riemann solver function for high-order RKDG methods, a one-dimensional numerical investigation was performed. Three traditional hydraulic problems were computed by this collection of solvers cooperated with high-order RKDG methods. A comparison of the performance of the solvers was carried out discussing the issue of -errors magnitude, CPU time cost, discontinuity resolution and source term effects.
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Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 2 • February 2008
Pages: 243 - 255
Copyright
© 2008 ASCE.
History
Received: Jul 16, 2006
Accepted: Jun 19, 2007
Published online: Feb 1, 2008
Published in print: Feb 2008
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