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

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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.