A well-balanced Runge-Kutta discontinuous Galerkin method for the Euler equations in isothermal hydrostatic state under gravitational field

Abstract

This article presents a well-balanced Runge-Kutta discontinuous Galerkin method for the Euler equations with gravitation and in the isothermal hydrostatic state. To achieve the well-balanced feature, we develop a decomposition algorithm backed by a novel auxiliary function. Using the decomposition algorithm, we successfully build well-balanced numerical fluxes and achieve novel discretizations to the source term, then realize the well-balancedness ultimately. A series of examples show the well-balanced feature, the high-order accuracy, and the high resolution.