Mathematical Sciences: Advanced Numerical Methods for Problems in the Physical Sciences

数学科学：物理科学问题的高级数值方法

• 批准号: 9404410
• 负责人: Elbridge Puckett
• 金额: $ 10.62万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404410&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Advanced; Numerical; Methods

Puckett The investigator undertakes the design, development and application of numerical methods for modeling fluid flows in which an essential feature of the flow is the presence of a moving boundary or interface. These methods are designed to study four specific problem areas: flow in ink jet dispensing devices, convection in weld pools, flames in compressible fluid flow, and high-velocity impact events in the geosciences. Work on these applications is conducted in close collaboration with experts in the relevant disciplines. The numerical methods are based on a collection of second-order "Godunov" methods for solving the equations of motion and second-order volume-of-fluid interface tracking algorithms for modeling the motion of the material interface. This methodology is coupled to a Cartesian grid method dor modeling arbitrary boundary geometries and an adaptive mesh refinement algorithm for locally concentrating computational effort in regions where it is most needed to achieve a given level of accuracy. The project aims to produce a collection of numerical methods that will enable researchers in the applied sciences and industry to model a broad class of problems that involve the motion of a material interface with confidence that the numerical results yield reliable quantitative data that is in good agreement with experiment. A second goal is to develop students who have a thorough understanding of this methodology and who can create new models and numerical methods based on these models to address problems that arise in science and industry. Computer models are an increasingly important part of the product design cycle in an ever increasing number of industries. Device simulation models are now routinely used in the semiconductor industry while the Boeing 777 is being called the first airplane to be designed on a computer. These models can reduce the product design cycle by months and sometimes years. However, there are still many importa nt industrial R&D problems for which current numerical methodology is either inadequate or nonexistent. One such class includes problems that are characterized by the presence of an interface between two materials or between different phases of a material. Examples include fluid jetting devices, mold filling and casting, etching of semiconductor devices, and thin film coatings. The goal of this research is to develop a new generation of advanced numerical methods for modeling such problems. These methods are designed to model four specific applications: flow in fluid jetting devices, convection in weld pools, flames in compressible fluid flow, and high-velocity impact events. Work on these applications is conducted in close collaboration with experts in the relevant disciplines. For example, the research on fluid jetting devices is conducted in collaboration with scientists at Xerox's Wilson Research Center in Rochester, NY and at MicroFab Inc. in Plano, TX. The first goal of the project is to produce a collection of numerical methods that will enable researchers in the applied sciences and industry to model a broad class of problems that involve the motion of a material interface, with confidence that the numerical results yield reliable quantitative data that is in good agreement with experiment. The second goal is to meet the ever increasing demand for scientists who are experts in the design and use of computational models of industrial processes by training students in all aspects of this field. This training includes student internships in industrial laboratory settings.

Puckett 研究人员负责设计，开发和应用模拟流体流动的数值方法，其中流动的一个基本特征是存在移动边界或界面。 这些方法的目的是研究四个具体的问题领域：在喷墨点胶设备，对流焊池，火焰中的可压缩流体流动，和高速冲击事件的地球科学。 这些应用程序的工作是与相关学科的专家密切合作进行的。 数值方法是基于一个集合的二阶“Goddom”的方法来解决的运动方程和二阶体积的流体界面跟踪算法建模的材料界面的运动。 这种方法是耦合到笛卡尔网格方法或建模任意边界几何形状和自适应网格细化算法局部集中的计算工作，它是最需要达到给定的精度水平的区域。 该项目旨在产生一系列数值方法，使应用科学和工业领域的研究人员能够对涉及材料界面运动的广泛一类问题进行建模，并确信数值结果产生与实验吻合良好的可靠定量数据。 第二个目标是培养对这种方法有透彻理解的学生，他们可以根据这些模型创建新的模型和数值方法，以解决科学和工业中出现的问题。 在越来越多的行业中，计算机模型是产品设计周期中越来越重要的一部分。 半导体行业现在经常使用器件仿真模型，而波音777被称为第一架在计算机上设计的飞机。 这些模型可以将产品设计周期缩短数月甚至数年。 然而，仍然有许多重要的工业R D问题，目前的数值方法是不够的或不存在。 其中一类问题的特征在于两种材料之间或材料的不同相之间存在界面。 实例包括流体喷射装置、模具填充和铸造、半导体装置的蚀刻和薄膜涂层。 本研究的目标是开发新一代的先进的数值方法来模拟这样的问题。 这些方法的目的是模拟四个具体的应用：流体喷射装置中的流动，焊接池中的对流，可压缩流体流中的火焰，以及高速冲击事件。 这些应用程序的工作是与相关学科的专家密切合作进行的。 例如，关于流体喷射装置的研究是与位于纽约州罗切斯特的施乐威尔逊研究中心和MicroFab公司的科学家合作进行的。位于德克萨斯州普莱诺。 该项目的第一个目标是产生一系列数值方法，使应用科学和工业领域的研究人员能够对涉及材料界面运动的广泛一类问题进行建模，并确信数值结果产生的可靠定量数据与实验结果吻合良好。 第二个目标是通过培训学生在这一领域的各个方面，满足对科学家的日益增长的需求，他们是设计和使用工业过程计算模型的专家。 该培训包括学生在工业实验室环境中的实习。