Well-balanced central schemes for the one and two-dimensional Euler systems with gravity

被引：12

作者：

Kanbar, F. ^{[1
,2
]}

Touma, R. ^{[2
]}

Klingenberg, C. ^{[1
]}

机构：

[1] Univ Wuezburg, Math, Wurzburg, Germany

[2] Lebanese Amer Univ, Math, Beirut, Lebanon

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 156卷

关键词：

Euler equations; Unstaggered central schemes; Well-balanced schemes; Stationary solutions; NONOSCILLATORY CENTRAL SCHEMES; UNSTAGGERED CENTRAL SCHEMES; FINITE-VOLUME EXTENSION; NESSYAHU-TADMOR SCHEME; UNSTRUCTURED GRIDS; HYPERBOLIC SYSTEMS; EQUATIONS; IDEAL;

D O I：

10.1016/j.apnum.2020.05.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we develop a family of central schemes for the one and two-dimensional systems of Euler equations with gravitational source term. The proposed schemes are unstaggered, second-order, central finite volume schemes that avoid solving Riemann problems at the cell interfaces and avoid switching between an original and a staggered grid. The main feature of the schemes developed here is that they are capable of preserving any steady state of the Euler with gravity system up to machine accuracy by updating the numerical solution in terms of a relevant reference solution. The methodology proposed results in a well-balanced scheme capable of capturing any steady state. Our scheme is then implemented and used to solve classical problems from the recent literature. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：608 / 626

页数：19