RUI: Spectral Methods and Their Combinations with the Finite Element Method for Chemically Reacting Flows and PDEson Nonsmooth Domains

谱方法在瞬变和湍流研究中得到了广泛的应用，但由于它们不能处理非光滑区域上的不连续问题，限制了它们的应用范围。这个项目将有助于减少这两个限制。它将设计无振荡谱方法来模拟化学反应流动，特别是爆轰波和从燃烧到爆轰的转变。谱激波拟合法将被用来研究爆轰波和扰动的相互作用。本质上，非振荡近似将被用来解决解中的高梯度和不连续性。通过将谱单元方法与p-和h-p版本的有限元方法相结合，将放宽区域限制。然后将组合方法应用于非光滑区域上的一般椭圆型方程，并将结果用于非规则流道中的流动模拟。

Spectral methods have been widely applied to the study of transient and turbulent flows, yet their scope of application has been limited by their inability to treat discontinuous problems on nonsmooth domains. This project will serve to reduce these two restrictions. It will design oscillation-free spectral methods to simulate chemically reacting flows, especially the detonation waves and the transition from deflagration to detonation. Spectral shock fitting methods will be applied to study the interaction of a detonation wave and disturbances. Essentially non-oscillatory approximations will be used to resolve the high gradients and discontinuities in the solutions. The domain restrictions will be eased by combining the spectral element methods with the p- and the h-p version of the finite element method. 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.