Samet Y  Kadioglu, Postdoctoral Fellow, North Carolina State University

A Fourth Order PPM Finite Volume Based Spectral Deferred Correction Method For Solving Conservation Laws

Abstract:  We present a new fourth order PPM (Piecewise Parabolic Method) finite volume based SDC (Spectral Deferred Cor-
rection) method for solving conservation laws. We use PPM framework to define edge averaged quantities which are used to evaluate fluxes. We use a fourth order Spectral Deferred Correction technique to update the state variables in time. The method is tested by solving variety of problems. The results indicate that we achieved fourth order of accuracy in time and space when the flow is smooth. The results also demonstrate the shock capturing ability of our newly proposed technique when the flow experiences shock waves.