High-order well-balanced finite volume schemes for the Euler equations with gravitation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:378

Article

Grosheintz-Laval, L.¹  Kappeli, R.¹ 

[1] Swiss Fed Inst Technol, Dept Math, SAM, CH-8092 Zurich, Switzerland

关键词: Numerical methods;    Hydrodynamics;    Source terms;    Well-balanced schemes;   

DOI  :  10.1016/j.jcp.2018.11.018

来源: Elsevier

【 摘 要 】

A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of isentropic hydrostatic equilibria. It is based on a novel local hydrostatic reconstruction, which, in combination with any standard high-order accurate reconstruction procedure, achieves genuine high-order accuracy for smooth solutions close or away from equilibrium. The resulting scheme is very simple and can be implemented into any existing finite volume code with minimal effort. Moreover, the scheme is not tied to any particular form of the equation of state, which is crucial for example in astrophysical applications. Several numerical experiments were performed with a third-order accurate reconstruction. They demonstrate the robustness and high-order accuracy of the scheme nearby and out of hydrostatic equilibrium. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free