Research on Hyperbolic Problems

数学科学：双曲问题的研究 金本研究计画系关于流体力学、化学反应流及稀薄气体动力学之双曲型方程组之数值方法设计与分析。 工作将在三个主要项目上进行：研究具有超特征松弛的双曲系统，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伯内特方程。 这些项目将大大提高对各种重要物理系统的理解，并为它们的模拟提供有效的数值方法。随着现代计算机的发展，高性能科学计算在科学研究中发挥着核心作用。 这里研究的物理和工业问题涉及液体和气体的流动行为，不能用传统方法解决。 然而，数值计算是一个有效的工具，以获得很好的近似这些问题的解决方案。 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.