A local discontinuous Galerkin method for a doubly nonlinear diffusion equation arising in shallow water modeling |
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| Authors: | Mauricio Santillana Clint Dawson |
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| Affiliation: | 1. Water Resources Management and Modeling of Hydrosystems, Department of Civil Engineering, Technische Universität Berlin, TIB 1-B14, Gustav-Meyer-Allee 25, 13355 Berlin, Germany;2. School of Civil Engineering & Geosciences, Newcastle University, Newcastle upon Tyne NE1 7RU, UK;1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, United States;2. Computational Health Informatics Program, Boston Children''s Hospital, Boston, MA 02115, United States;3. Laboratory for Climate and Ocean-Atmosphere Sciences, Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing, 100871, China;1. Centre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds, United Kingdom;2. School of Mathematics, University of Leeds, Leeds, United Kingdom;3. School of Earth and Environment, University of Leeds, Leeds, United Kingdom |
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| Abstract: | In this paper, we study a local discontinuous Galerkin (LDG) method to approximate solutions of a doubly nonlinear diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW). This equation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases: the Porous Medium equation and the parabolic p-Laplacian. Continuous in time a priori error estimates are established between the approximate solutions obtained using the proposed LDG method and weak solutions to the DSW equation under physically consistent assumptions. The results of numerical experiments in 2D are presented to verify the numerical accuracy of the method, and to show the qualitative properties of water flow captured by the DSW equation, when used as a model to simulate an idealized dam break problem with vegetation. |
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