High-order curvilinear meshing using a thermo-elastic analogy
High-order curvilinear meshing using a thermo-elastic analogy
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DOI：
10.1016/j.cad.2015.09.007
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发表时间：
2016-03-01
影响因子：
4.3
通讯作者：
Peiro, J.
中科院分区：
文献类型：
--
作者：
Moxey, D.;Ekelschot, D.;Peiro, J.
随着高阶方法在学术界和工业界越来越流行，生成与复杂几何边界一致的曲线网格仍然是一个巨大的挑战。传统的低阶方法使用平面单元，而高阶方法在单元中引入曲率，如果添加得太天真，可能会导致单元自交。在过去的几年里，已经设计了几种曲线网格生成技术来解决这个问题，利用网格变形来移动网格的内部节点，以适应边界上的曲率。其中许多是基于弹性模型，其中网格被视为实体，并根据线性或非线性应力张量进行变形。但是，这类方法通常不会显式控制结果网格中元素的有效性。在这篇文章中，我们提出了这一弹性公式的一个扩展，即在“热”或“冷”单元变形时引入热应力项。我们概述了一个概念验证实现，并通过考虑二维和三维的例子表明，采用热弹性类比导致了额外程度的稳健性。(C)2015年提交人。爱思唯尔有限公司出版。
With high-order methods becoming increasingly popular in both academia and industry, generating curvilinear meshes that align with the boundaries of complex geometries continues to present a significant challenge. Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added naively, cause the element to self-intersect. Over the last few years, several curvilinear mesh generation techniques have been designed to tackle this issue, utilizing mesh deformation to move the interior nodes of the mesh in order to accommodate curvature at the boundary. Many of these are based on elastic models, where the mesh is treated as a solid body and deformed according to a linear or non-linear stress tensor. However, such methods typically have no explicit control over the validity of the elements in the resulting mesh. In this article, we present an extension of this elastic formulation, whereby a thermal stress term is introduced to 'heat' or 'cool' elements as they deform. We outline a proof-of-concept implementation and show that the adoption of a thermo-elastic analogy leads to an additional degree of robustness, by considering examples in both two and three dimensions. (C) 2015 The Authors. Published by Elsevier Ltd.