High order finite volume WENO schemes for the Euler equations under gravitational fields

JOURNAL OF COMPUTATIONAL PHYSICS

卷:316

Article

Li, Gang¹  Xing, Yulong² 

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

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

关键词: Finite volume schemes;    Euler equations;    WENO schemes;    Well-balanced property;    High order accuracy;    Gravitational field;   

DOI  :  10.1016/j.jcp.2016.04.015

来源: Elsevier

【 摘 要 】

Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free