Well-balanced discontinuous Galerkin methods with hydrostatic reconstruction for the Euler equations with gravitation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:352

Article

Li, Gang¹  Xing, Yulong² 

[1] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China

[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

关键词: Euler equations;    Polytropic equilibrium;    Discontinuous Galerkin methods;    Well-balanced property;    High order accuracy;    Gravitational field;   

DOI  :  10.1016/j.jcp.2017.09.063

来源: Elsevier

【 摘 要 】

Many interesting astrophysical and atmospheric problems involve flows near the hydrostatic equilibrium state where the pressure gradient is balanced by the gravitational force. In this paper, we design high order well-balanced discontinuous Galerkin methods for the Euler equations with gravitation, which can preserve the discrete polytropic and isothermal hydrostatic balance states exactly. To achieve the well-balancedness, we propose to combine the numerical fluxes based on a generalized hydrostatic reconstruction, with an equilibrium state recovery technique and a novel source term approximation. Extensive one-and two-dimensional numerical examples are shown to demonstrate the performance of our well-balanced methods, and comparison with non-well-balanced results is included to illustrate the importance of maintaining the balance between pressure gradient and gravitational force numerically. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free