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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.

本研究计画旨在发展有效的动态网格调适策略，以应用于物理科学中演化问题的数值模拟。网格自适应是科学和工程中基于网格的数值模拟不可缺少的工具。它的基本思想是把更多的网格节点在大的解决方案变化的区域比那些解决方案是光滑的。以这种方式，需要更少的网格节点来达到指定的精度水平，从而获得显著的经济效益。动态网格自适应是一种网格自适应，它移动网格节点来跟踪物理问题的动态特征。动态网格自适应方法在时间上的连续性使其成为演化问题数值求解的自然选择，本文的研究重点是提高动态网格自适应的效率。课程包括移动网格上的偏微分方程的时间积分的调查，施瓦茨波形移动网格方法的发展，以及简单而有效的网格方程求解器的发展。所有的研究将针对液晶模型和相变问题所产生的演化偏微分方程。这些问题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这些问题的解奇点的形成和移动界面的传播提供一个强有力的工具。研究生将积极参与研究项目。学生的训练将受益于大规模计算以及理论研究。