Abstract
In this paper, we present high order discontinuous Galerkin methods for the Ripa model. This model maintains the steady state. To achieve the well-balanced property, we first reformulate the governing equations and propose to construct a novel source term approximation. In addition, we apply a flux modification technique to construct the numerical fluxes. Rigorous numerical analysis as well as extensive one- and two-dimensional numerical results all verify that the proposed methods are well-balanced for the steady state, keep genuinely high order accuracy in smooth regions for smooth solutions, and enjoy good resolutions for discontinuous solutions.
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