权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Grid generation and multigrid schemes for spectral element methods in curved domains

弯曲域谱元法的网格生成和多重网格方案

基本信息

批准号：
232080977
负责人：
Privatdozent Dr.-Ing. Jörg Stiller
金额：
--
依托单位：
Institut für Strömungsmechanik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/232080977?language=en
关键词：
Grid generation multigrid schemes spectral

项目摘要

The objective of the project is to render the spectral element method competitive to classical lower order discretization methods for applications involving curved domains. To achieve this, we propose an integral approach that tackles the principal weaknesses of previous methods. The key components are as follows: 1) Stable and convergent methods for constructing nearly isometric patches starting from a linear triangulation of the surface.2) A moving mesh method for generating a boundary-conforming curved grid with built-in metric control.3) Spectral element multigrid techniques with near optimal complexity for implicit equations arising from discretization moving mesh and incompressible flow problems. A major challenge in 1) is to devise how boundary curves between surface vertices must be constructed in order to aid the creation of well-behaved patches while maintaining optimal accuracy. Based on this prerequisite, the patch construction itself will be optimized via suitable parameterization of sampling points. This approach allows for improving the metric without loss of precision. Once the surface grid is fixed, the moving mesh method serves to generate a well-behaved, boundary fitting spatial grid. In contrast to the elastic analogy recently advocated by Persson and Preraire, the moving mesh method has the advantage of direct metric control and higher flexibility because of the loose coupling between material elements. An open issue that will be addressed is the proper imposition of time-dependent boundary conditions, which drive the transition from the polyhedral toward a curved grid. In addition to this we aim at efficient implicit solution techniques for the spectral element formulation of the moving mesh method. This work will be fueled considerably by the development of structure-exploiting multigrid methods in the third part of the project. Finally these methods will be used as a building block for prototyping a spectral element flow solver that demonstrates the capability of the overall approach.

该项目的目标是使谱元素方法在涉及曲线域的应用中与经典的低阶离散化方法相竞争。为了实现这一点，我们提出了一种综合方法，解决了以前方法的主要缺点。主要内容如下：1)从曲面的线性三角剖分出发构造近似等距面片的稳定收敛方法；2)内建度量控制的移动网格生成边界协调曲面网格的移动网格方法；3)离散、移动网格和不可压缩流动问题隐式方程的谱单元多重网格技术。1)中的一个主要挑战是设计如何构建曲面顶点之间的边界曲线，以便在保持最佳精度的同时帮助创建行为良好的面片。在此前提下，通过对采样点进行适当的参数化处理，对面片结构本身进行优化。这种方法允许在不损失精度的情况下改进度量。一旦固定了曲面网格，移动网格方法就可以生成行为良好、边界适配的空间网格。与Persson和Preraire最近倡导的弹性类比相比，由于材料单元之间的松散耦合，移动网格法具有直接度量控制和更高的灵活性的优点。一个有待解决的问题是适当地施加依赖于时间的边界条件，这些条件推动了从多面体到曲线网格的过渡。此外，我们还针对移动网格法的谱元素公式，提出了有效的隐式求解技术。该项目第三部分开发的结构开发多重网格法将极大地推动这项工作。最后，这些方法将被用作原型的谱元流解算器的构建块，以展示整体方法的能力。