High order well-balanced discontinuous Galerkin methods for shallow water flow under temperature fields

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.