Asymptotic preserving schemes on conical unstructured 2D meshes,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.)

Asymptotic preserving schemes on conical unstructured 2D meshes
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-05-10 , DOI: 10.1002/fld.4997
X. Blanc ₁ , V. Delmas ₂ , P. Hoch ₂

Affiliation

In this article, we consider the hyperbolic heat equation. This system is linear hyperbolic with stiff source terms and satisfies a diffusion limit. Some finite volume numerical schemes have been proposed which reproduce this diffusion limit. Here, we extend such schemes, originally defined on polygonal meshes, to conical meshes (using rational quadratic Bezier curves). We obtain really new schemes that do not reduce to the polygonal version when the conical edges tend to straight lines. Moreover, these schemes can handle curved unstructured meshes so that geometric error on initial data representation is reduced and geometry of the domain is improved. Extra flux coming from conical edge (through his midedge point) has a deep impact on the stabilization when compared with the original polygonal scheme. Cross-stencil phenomenon of polygonal scheme has disappeared, and issue of positivity for the diffusion problem (although unresolved on distorted mesh and/or with varying cross-section) has been in some sense improved.

中文翻译：

锥形非结构化二维网格的渐近保持方案

在本文中，我们考虑双曲热方程。该系统是具有刚性源项的线性双曲线系统，并且满足扩散限制。已经提出了一些重现这种扩散极限的有限体积数值方案。在这里，我们将这些最初定义在多边形网格上的方案扩展到锥形网格（使用有理二次贝塞尔曲线）。当锥形边缘趋于直线时，我们获得了真正新的方案，这些方案不会减少到多边形版本。此外，这些方案可以处理弯曲的非结构化网格，从而减少初始数据表示的几何误差并改善域的几何形状。与原始多边形方案相比，来自锥形边缘（通过其中间点）的额外通量对稳定性有很大影响。

更新日期：2021-07-01

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