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On the Use of Anisotropic Triangles with Mixed Finite Elements: Application to an 'Immersed' Approach for Incompressible Flow Problems

机译:关于混合有限元各向异性三角形的应用:在不可压缩流动问题的“沉浸式”方法中的应用

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摘要

In this chapter, we discuss the use of some common mixed finite elements in the context of a locally anisotropic remeshing strategy, close in philosophy to "immersed" approaches for interface problems. A characteristic of the present method is the presence of highly flat triangles. Such a distinctive feature may imply stability issues for mixed elements with incompressible flow problems. First, we present a review of the literature dealing with interface problems and we illustrate these results with a simple 1D framework alongside of numerical tests. Second, we present the locally anisotropic remeshing approach for interface problems in 2D with a focus on the incompressible Stokes problem. We then present numerical tests to show stability issues of common mixed elements, as well as possible stable ones. We also deal with conditioning issues. Finally, we illustrate the results with two applications, including the fluid-structure interaction of a rotational rigid bar.
机译:在本章中,我们将讨论在局部各向异性重网格化策略中使用某些常见的混合有限元,在哲学上与界面问题的“沉浸式”方法相近。本方法的特征是高度平坦的三角形的存在。这种独特的特征可能暗示具有不可压缩流动问题的混合元件的稳定性问题。首先,我们介绍有关接口问题的文献,并通过简单的一维框架以及数值测试来说明这些结果。其次,我们针对2D界面问题提出了局部各向异性的网格划分方法,重点是不可压缩的Stokes问题。然后,我们提出数值测试,以显示常见混合元素以及可能稳定元素的稳定性问题。我们还处理条件问题。最后,我们用两个应用程序说明了结果,包括旋转刚性杆的流固耦合。

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  • 会议地点 Udine(IT)
  • 作者单位

    Department of Civil Engineering and Architecture, University of Pavia, Pavia, Italy;

    Department of Medicine, Emory University, Atlanta, GA, USA;

    Department of Civil Engineering and Architecture, University of Pavia, Pavia, Italy,Institute for Advanced Study, Technische Universitat Muenchen, Munchen, Germany;

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  • 正文语种 eng
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