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

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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.