Deformation Methods for Grid Adaptation

网格自适应的变形方法

• 批准号: 9732742
• 负责人: Guojun Liao
• 金额: $ 18.6万
• 依托单位: University of Texas at Arlington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9732742&HistoricalAwards=false
• 关键词: Deformation; Methods; Grid; Adaptation

DMS-9732742Guojun LiaoA key factor to the success of numerical simulation of scientific and engineering problems is that of grid generation of the physical domains. The objective of the project is to develop an adaptive grid generation method that can be used with various numerical schemes such as finite element, finite difference, etc. Our method is based on sophisticated mathematics and its numerical implementation is straightforward. It is the deformation method which redistributes the grid points according to the physical variables that are being simulated. A monitor function is calculated which is small where the error is large. The deformation method then moves each grid point according to the monitor function so that the new grid will be concentrated where the need for better resolution exists to reduce the error. Model problems from fluid dynamics and other important applications will be simulated on such moving grids. We will demonstrate that the method is capable of generating grids that are adapted to the fine features of the physical variables such as shock waves, moving fronts, and boundary layers, etc.This project is aimed to greatly enhance our ability to simulate large scale computational problems that are crucial to the national strategic interests. The advance of computing technology allows us to simulate some real world problem without conducting costly experiments. But the needs for accurate and efficient simulation far exceed the most powerful computers of today. A lot of simplification and upgrading have to be made to stay within the limit of today's computing capacity. Fixed grids are wasteful in computing resource. Our research will lead to software that can automatically put more points to the regions where and when the physical variables change rapidly without adding new points. This would be very useful for high performance computing and the numerical simulation of material science, environment problems, manufacturing process and other fields that require a grid. By working in the project, mathematics and engineering students will gain first hand experience on the application of mathematics to the solution of engineering problem. Advanced degrees will be granted to graduate students who make significant contributions to the project after their completion of course work.

科学与工程问题数值模拟成功的关键是物理域网格的生成。 该项目的目标是开发一种自适应网格生成方法，可用于各种数值方案，如有限元，有限差分等，我们的方法是基于复杂的数学，其数值实现是简单的。 它是根据被模拟的物理变量重新分布网格点的变形方法。 在误差大的地方计算一个小的监控函数。 然后，变形方法根据监控函数移动每个网格点，使得新网格将集中在需要更好分辨率的地方，以减少误差。流体动力学和其他重要应用的模型问题将在这种移动网格上进行模拟。 我们将证明该方法能够生成适合于激波、运动锋和边界层等物理变量精细特征的网格。该项目旨在大大提高我们模拟对国家战略利益至关重要的大规模计算问题的能力。 计算技术的进步使我们能够模拟一些真实的世界问题，而无需进行昂贵的实验。 但是，对准确和有效模拟的需求远远超过了当今最强大的计算机。 必须进行大量的简化和升级，以保持在今天的计算能力的限制之内。 固定网格是计算资源的浪费。 我们的研究将导致软件，可以自动把更多的点的区域，当物理变量迅速变化，而不添加新的点。 这对于高性能计算以及材料科学、环境问题、制造过程等需要网格的领域的数值模拟都是非常有用的。 通过在项目中工作，数学和工程专业的学生将获得第一手经验，数学的应用，以解决工程问题。 高级学位将授予研究生谁作出重大贡献的项目完成后，他们的课程工作。