期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 232, 期 1, 页码 46-67出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.06.006
关键词
Adaptive finite elements; Discontinuous Galerkin methods; Semi-implicit discretizations; Semi-Lagrangian discretizations; Shallow water equations
资金
- Abdus Salam International Centre for Theoretical Physics
- Regione Lombardia
- Italian Ministry of Research and Education
- GNCS project Sviluppi teorici ed applicativi dei metodi Semi-Lagrangiani
A semi-implicit and semi-Lagrangian discontinuous Galerkin method for the shallow water equations is proposed, for applications to geophysical scale flows. A non conservative formulation of the advection equation is employed, in order to achieve a more treatable form of the linear system to be solved at each time step. The method is equipped with a simple p-adaptivity criterion, that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution. Numerical results show that the method captures well the main features of gravity and inertial gravity waves, as well as reproducing correct solutions in nonlinear test cases with analytic solutions. The accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree. (C) 2012 Elsevier Inc. All rights reserved.
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