Efficient dynamic mesh adaptation for numerical simulation of evolutionary problems arising from physical science

用于物理科学进化问题数值模拟的高效动态网格自适应

基本信息

批准号：
0712935
负责人：
Weizhang Huang
金额：
$ 13万
依托单位：
University of Kansas Center for Research Inc
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2007
资助国家：
美国
起止时间：
2007-09-01 至 2011-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0712935&HistoricalAwards=false
关键词：
Efficient dynamic mesh adaptation numerical

项目摘要

This research project is to develop efficient dynamic mesh-adaptation strategies for the numerical simulation of evolutionary problems arising from physical science. Mesh adaptation is an indispensable tool for use in mesh-based numerical simulation in science and engineering. Its basic idea is to put more mesh nodes in regions of large solution variation than those where the solution is smooth. In this way, fewer mesh nodes are required to reach a specified level of accuracy and thus significant economies are gained. Dynamic mesh adaptation is a type of mesh adaptation which moves mesh nodes around to follow the dynamic features of the physical problem. Its continuous nature in time makes a dynamic mesh-adaptation method the natural choice of method for use in the numerical solution of evolutionary problems.The proposed research focuses on improving the efficiency of dynamic mesh adaptation. Topics of study include the investigation of time integration of partial differential equations on moving meshes, the development of the Schwarz waveform moving-mesh method, and the development of simple and efficient solvers for mesh equations. All studies will be targeted on evolutionary partial differential equations arising from liquid-crystal models and phase-change problems. These problems have many important industrial applications and have attracted considerable interest among scientists. Successful completion of this project will provide a powerful tool for studying the formation of solution singularities and the propagation of moving interfaces arising from these problems. Graduate students will be actively involved in the research project. Students' training will benefit from large-scale computations as well as theoretical studies.

该研究项目是为了制定有效的动态网状适应策略，以模拟物理科学引起的进化问题。网格改编是一种必不可少的工具，用于在科学和工程中基于网格的数值模拟中使用。它的基本思想是将更多的网状节点放在大型溶液变化的区域中，而解决方案则是平滑的。以这种方式，要达到指定的准确性水平，因此需要更少的网格节点，从而获得了重要的经济体。动态网格适应是一种网格适应，它可以移动网格节点，以遵循物理问题的动态特征。它的持续性质使动态网状适应方法是在进化问题的数值解决方案中使用的自然选择。拟议的研究重点是提高动态网格适应的效率。研究主题包括研究移动网格的部分微分方程，Schwarz波形移动网格方法的发展以及用于网格方程的简单有效求解器的开发。所有研究都将针对由液体晶体模型和相变问题引起的进化偏微分方程。这些问题具有许多重要的工业应用，并引起了科学家的极大兴趣。该项目的成功完成将为研究解决方案奇点的形成以及由这些问题引起的移动界面的传播提供强大的工具。研究生将积极参与研究项目。学生的培训将受益于大规模计算以及理论研究。