Research on Hyperbolic Problems

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Mathematical Sciences: Research on Hyperbolic ProblemsAbstract0072374 JinThis research project is concerned with design and analysis of numerical methods for hyperbolic systems arising from fluid dynamics, chemically reacting flows, and rarefied gas dynamics. Work will be done on three main projects: study of hyperbolic systems with supercharacteristic relaxations, development of random projection methods for reacting flows, and study of the relaxed Burnett equations for rarefied gas dynamics. These projects will significantly enhance understanding of a variety of important physical systems and will provide effective numerical methods for their simulation.With the development of modern computers, high performance scientific computation has been playing a central role in scientific investigation. The physical and industrial problems under study here concern the behavior of flowing liquids and gasses and are not amenable to solution by traditional methods. Nevertheless, numerical computation is an effective tool to obtain very good approximations to the solutions of these problems. This project will advance the ability to utilize high performance computers to solve these and other problems of importance.