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

Puckett研究员负责设计、开发和应用数值方法来模拟流体流动，其中流动的一个基本特征是存在移动的边界或界面。这些方法旨在研究四个特定的问题领域：喷墨点胶设备中的流动、焊接熔池中的对流、可压缩流体流动中的火焰以及地球科学中的高速撞击事件。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。数值方法基于求解运动方程的二阶Godunov方法和模拟材料界面运动的二阶流体体积跟踪算法的集合。该方法与笛卡尔网格法和自适应网格精化算法相结合，用于在最需要达到给定精度水平的区域中局部集中计算工作量。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模拟涉及材料界面运动的广泛类别的问题，并确信数值结果产生可靠的定量数据，与实验很好地吻合。第二个目标是培养学生对这种方法有透彻的理解，并能够基于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，计算机模型在产品设计周期中扮演着越来越重要的角色。器件模拟模型现在半导体行业中司空见惯，而波音777被称为第一架在计算机上设计的飞机。这些型号可以将产品设计周期缩短数月，有时甚至数年。然而，仍然有许多重要的工业R&D问题，现有的数值方法不是不充分就是不存在。一个这样的类别包括以两种材料之间或一种材料的不同相之间存在界面为特征的问题。例如，流体喷射装置、充模和铸造、半导体器件的蚀刻和薄膜涂层。这项研究的目标是开发新一代先进的数值方法来模拟这类问题。这些方法被设计用来模拟四种特定的应用：流体喷射装置中的流动、焊接熔池中的对流、可压缩流体流动中的火焰以及高速碰撞事件。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，流体喷射设备的研究是与位于纽约罗切斯特的施乐威尔逊研究中心和位于德克萨斯州普莱诺的MicroFab Inc.的科学家合作进行的。该项目的第一个目标是产生一组数值方法，使应用科学和工业中的研究人员能够对涉及材料界面运动的广泛类别的问题进行建模，并确信数值结果产生与实验完全一致的可靠定量数据。第二个目标是通过培训学生在这一领域的所有方面来满足日益增长的对设计和使用工业过程计算模型的科学家的需求。这项培训包括在工业实验室环境中实习。

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.