An explicit finite volume scheme on staggered grids for the Euler equations: Unstructured meshes, stability analysis, and energy conservation,International Journal for Numerical Methods in Fluids

当前位置： X-MOL 学术 › Int. J. Numer. Methods Fluids › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

An explicit finite volume scheme on staggered grids for the Euler equations: Unstructured meshes, stability analysis, and energy conservation
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-09-22 , DOI: 10.1002/fld.5048
Thierry Goudon ₁ , Julie Llobell ₁ , Sebastian Minjeaud ₁

Affiliation

We set up a numerical strategy for the simulation of the Euler equations, in the framework of finite volume staggered discretizations where numerical densities, energies, and velocities are stored on different locations. The main difficulty relies on the treatment of the total energy, which mixes quantities stored on different grids. The proposed method is strongly inspired, on the one hand, from the kinetic framework for the definition of the numerical fluxes, and, on the other hand, from the discrete duality finite volume (DDFV) framework, which has been designed for the simulation of elliptic equations on complex meshes. The time discretization is explicit and we exhibit stability conditions that guaranty the positivity of the discrete densities and internal energies. Moreover, while the scheme works on the internal energy equation, we can define a discrete total energy which satisfies a local conservation equation. We provide a set of numerical simulations to illustrate the behavior of the scheme.

中文翻译：

欧拉方程交错网格上的显式有限体积方案：非结构化网格、稳定性分析和能量守恒

我们在有限体积交错离散化的框架内建立了一个用于模拟欧拉方程的数值策略，其中数值密度、能量和速度存储在不同的位置。主要的困难在于对总能量的处理，它混合了存储在不同网格上的数量。所提出的方法一方面受到数值通量定义的动力学框架的强烈启发，另一方面受到离散对偶有限体积（DDFV）框架的启发，该框架专为模拟复杂网格上的椭圆方程。时间离散化是明确的，我们展示了保证离散密度和内能的正性的稳定性条件。此外，虽然该方案适用于内能方程，局部守恒方程。我们提供了一组数值模拟来说明该方案的行为。

更新日期：2021-09-22

点击分享查看原文

点击收藏

阅读更多本刊最新论文本刊介绍/投稿指南11