Research on Hyperbolic Problems

数学科学：双曲型问题的研究本研究项目致力于设计和分析由流体动力学、化学反应流动和稀薄气体动力学引起的双曲型系统的数值方法。将在三个主要项目上开展工作：研究具有超特征松弛的双曲组，发展反应流的随机投影方法，以及研究稀薄气体动力学的松弛Burnett方程。随着现代计算机的发展，高性能的科学计算在科学研究中发挥着越来越重要的作用。这里研究的物理和工业问题涉及流动的液体和气体的行为，不是传统方法所能解决的。然而，数值计算是获得这些问题解的非常好的近似值的有效工具。该项目将提高利用高性能计算机解决这些和其他重要问题的能力。

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.