RUI: Spectral Methods and Their Combination with the h-p Version of Finite Element Method for Chemically Reacting Flow and PDE's on Nonsmooth Domains

谱方法已广泛应用于瞬态和湍流的研究。但是由于不能处理不连续问题和非光滑域上的问题，严重限制了它们的应用范围。本项目旨在减少光谱方法的这两个限制。设计无振荡均匀高阶谱方法来模拟化学反应流动，特别是爆震波和爆燃到爆轰的过渡（DDT）。为了减轻域限制，谱方法和p-和hp版本的有限元方法将被结合起来。然后将该方法应用于非光滑区域上的一般椭圆方程，并将结果用于非光滑通道内的流动模拟。这些方法将在高性能计算机上实现。

Spectral methods have been widely applied for transient and turbulent flows. However their scope of application has been seriously limited by their inability to treat discontinuous problems and problems on nonsmooth domains. This project intends to reduce these two restrictions of spectral methods. Oscillation-free uniform high order spectral methods to simulate chemically reacting flows, especially the detonation waves and the transition from deflagration to detonation (DDT) will be designed. To ease the domain restrictions, spectral methods and the p- and the h-p version of the finite element methods will be combined. Then the combined method will be applied to general elliptic equations on nonsmooth domains and the results will be used to simulate flows in irregular channels. These methods will be implemented on high performance computers.