A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations |
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| Authors: | Maojun Li Philippe Guyenne Fengyan Li Liwei Xu |
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| Affiliation: | 1.College of Mathematics and Statistics,Chongqing University,Chongqing,People’s Republic of China;2.Institute of Computing and Data Sciences,Chongqing University,Chongqing,People’s Republic of China;3.Department of Mathematical Sciences,University of Delaware,Newark,USA;4.Department of Mathematical Sciences,Rensselaer Polytechnic Institute,Troy,USA;5.School of Mathematical Sciences,University of Electronic Science and Technology of China,Sichuan,People’s Republic of China |
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| Abstract: | In this paper, we consider the development of central discontinuous Galerkin methods for solving the nonlinear shallow water equations over variable bottom topography in one and two dimensions. A reliable numerical scheme for these equations should preserve still-water stationary solutions and maintain the non-negativity of the water depth. We propose a high-order technique which exactly balances the flux gradients and source terms in the still-water stationary case by adding correction terms to the base scheme, meanwhile ensures the non-negativity of the water depth by using special approximations to the bottom together with a positivity-preserving limiter. Numerical tests are presented to illustrate the accuracy and validity of the proposed schemes. |
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