Application of Distributed Adaptive Mesh Refinement Techniques to Problems Involving Diffusion

分布式自适应网格细化技术在涉及扩散问题中的应用

• 批准号: 9870384
• 负责人: William Allard
• 金额: $ 15万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-15 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870384&HistoricalAwards=false
• 关键词: Application; Distributed; Adaptive; Mesh; Refinement

A number of physical problems involve localized phenomenathat move in time, such as fluid fronts, interfaces and shocks.Often, these phenomena are not captured well by finite differencemethods on uniform grids. The investigators work on threeclasses of such problems: flow in porous media, particularlychemically enhanced aquifer remediation; thin film flow withfluid fronts due to vanishing diffusive fluxes; and excitablemedia, particularly the modeling of the propagation of electricalimpulses in the heart. All three of these problems involvediffusion; the diffusion can be nonlinear, subdiffusive orsuperdiffusive. The investigators develop efficient multileveliterative methods and adaptive mesh refinement tools to solvethese problems on parallel processor machines. The power of computers has dramatically increased sincethey were introduced a half century ago, and this improvement inperformance continues at a breathtaking pace. Nonetheless,although the public is generally unaware of this, thecomputational resources required to simulate many phenomena, likethe weather, greatly exceed those currently available. One wayto obtain a lot of computer power is to arrange for manycomputers to work simultaneously on a problem. However, it is adaunting task to program these computers so that they willcorrectly produce the desired simulation in a timely fashion. Inthis work, the investigators develop effective methods to usemany computers working together to simulate the flow ofcontaminants in the ground, the behavior of thin films, and theelectrophysiology of the heart. Groundwater contamination is asignificant environmental problem. Thin film problems arise inlubrication and in manufacturing processes. A fundamentalunderstanding of the electrical and muscular behavior of theheart is important and could lead to better control of themechanisms of arrhythmia.

许多物理问题涉及随时间移动的局部现象，如流体锋面、界面和冲击。通常，有限差分法在均匀网格上不能很好地捕捉到这些现象。研究人员研究了三类此类问题：多孔介质中的流动，特别是化学增强的含水层修复；由于扩散通量的消失，薄膜以流体前沿流动；以及可兴奋介质，特别是对心脏中电脉冲传播的建模。这三个问题都涉及扩散；扩散可以是非线性的、亚扩散的或超扩散的。研究人员开发了高效的多层迭代方法和自适应网格细化工具来解决并行处理器机器上的这些问题。自从半个世纪前计算机问世以来，它的能力已经大大增强，而且这种性能上的改进还在以惊人的速度继续着。然而，尽管公众通常没有意识到这一点，但模拟许多现象（如天气）所需的计算资源大大超过了目前可用的计算资源。获得大量计算机能力的一种方法是安排多台计算机同时处理一个问题。然而，对这些计算机进行编程，使它们能够及时正确地产生所需的模拟，这是一项适应任务。在这项工作中，研究人员开发了有效的方法，利用多台计算机协同工作来模拟污染物在地面上的流动、薄膜的行为和心脏的电生理。地下水污染是一个重大的环境问题。薄膜问题出现在润滑和制造过程中。对心脏电和肌肉行为的基本理解是重要的，可以更好地控制心律失常的机制。