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首页> 外文期刊>Journal of Computational Physics >High order finite volume WENO schemes for the Euler equations under gravitational fields
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High order finite volume WENO schemes for the Euler equations under gravitational fields

机译：引力场下Euler方程的高阶有限体积WENO格式。

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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.
机译：具有引力源项的欧拉方程用于模拟许多天体和大气现象。该系统允许静水力平衡，其中由压力产生的通量被重力源项精确抵消，并且两个常见的平衡是等温和多向静水力解决方案。精确保存这些平衡是合乎需要的，因为许多实际问题是这种平衡的微小扰动。在[22]中已经提出了高阶有限差分加权基本非振荡（WENO）方案，但是仅针对等温平衡状态。在本文中，我们设计了高阶均衡的有限体积WENO方案，该方案不仅可以精确地保持等温平衡，而且可以精确地保持多态静水平衡状态，并且对于一般解决方案保持真正的高阶精度。通过新颖的源项重新公式化和离散化，再加上均衡的数值通量，可以获得均衡的属性。进行了广泛的一维和二维仿真，以验证平衡良好的特性，高阶精度以及平滑和不连续解决方案的良好分辨率。 （C）2016 Elsevier Inc.保留所有权利。

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