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A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations
Author(s) -
Kesserwani Georges,
Mosé Robert,
Vazquez José,
Ghenaim Abdellah
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1879
Subject(s) - discontinuous galerkin method , riemann solver , benchmark (surveying) , runge–kutta methods , solver , shallow water equations , mathematics , flow (mathematics) , open channel flow , scheme (mathematics) , channel (broadcasting) , computer science , limiting , numerical analysis , mathematical optimization , finite volume method , finite element method , mathematical analysis , engineering , geometry , telecommunications , mechanical engineering , physics , structural engineering , geodesy , mechanics , geography
Abstract This paper comprises an implementation of a fourth‐order Runge–Kutta discontinuous Galerkin (RKDG4) scheme for computing the open‐channel flow equations. The main features of the proposed methodology are simplicity and easiness in the implementation, which may be of possible interest to water resources numerical modellers. A version of the RKDG4 is blended with the Roe Riemann solver, an adaptive high‐order slope limiting procedure, and high‐order source terms approximations. A comparison of the performance of the proposed method with lower‐order RKDG models is performed showing a benefit of considering the RKDG4 model. The scheme is applied to computerize the Saint Venant system by considering benchmark tests that have exact solutions. Finally, numerical results are illustrated discussing the performance of the proposed high‐order model. Copyright © 2008 John Wiley & Sons, Ltd.