Abstract 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.

中文翻译：

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具有重力的一维和二维欧拉系统的平衡中心方案

摘要 在本文中，我们为具有引力源项的欧拉方程的一维和二维系统开发了一系列中心格式。所提出的方案是非交错、二阶、中心有限体积方案，可避免在单元界面求解黎曼问题，并避免在原始网格和交错网格之间切换。这里开发的方案的主要特点是，它们能够通过根据相关参考解更新数值解来保持具有重力系统的欧拉的任何稳态，达到机器精度。所提出的方法产生了一个能够捕获任何稳定状态的平衡方案。然后实施我们的方案并用于解决最近文献中的经典问题。