HIGH ORDER ACCURACY METHODS FOR PDEs with SHOCKS and UNCERTAINTIES

The aim of t his project is the construction of efficient high fidelity schemes for systems of PDEs that contain shock waves. We advocate here the Discontinuous collocation method, i.e. multi-domain spe method with stable and conservative penalty interface conditions. In this work. the previously developed methodology is generalized to inhomogeneous grid to simulate the two dimensional supersonic injector-cavity system. Non-physical modes generated ;it t ho domain interfaces due to the spatial grid inhomogeneity is minimized using the new weighted multi-domain spectral penalty method. The method yields accurate and stable solutions of the injector-cavity system which agree well with experiments qualitatively. Through the direct numerical simulation of the injec tor-cavity system using the weighted method, the geometric effect of the cavity wall on the pressure fluctuation is investigated. It is shown that the recessed slanted cavity attenuates pressure fluctuations inside cavity enabling the cavity to act potentially as a stable flameholder for sen un jet engine. Multi-domain spectral penalty method for injector-recessed cavity system The major developments of the current work are 1. Stable and conservative penalty type interface conditions are derived for the inhomogeneous grid. 2. The weighted spectral penalty method is used to minimize the non-physical growth modes at the inhomogeneous domain interfaces. 3. The weighted spectral penalty method is applied successfully to the two dimensional reactive supersonic injector-recessed cavity äameholder. A crucial requirement from DNS computations of the injector-cavity system is to resolve the hydrogen jet injector without causing any instability or nonphysical growing modes at the domain interfaces. We use a smaller subdomain with higher order polynomials to resolve the narrow jet. In Figure 1 the local domain configuration