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C. Shu and S. Osher, “Efficient Implementation of Essen- tially Non-Oscillatory Shock Capturing Schemes II,” Jour- nal of Computational Physics, Vol. 83, No. 1, 1989, pp. 32-78. doi:10.1016/0021-9991(89)90222-2

has been cited by the following article:

• TITLE: A Gas Dynamics Method Based on the Spectral Deferred Corrections (SDC) Time Integration Technique and the Piecewise Parabolic Method (PPM)

  AUTHORS: Samet Y. Kadioglu

  KEYWORDS: Gas Dynamics, Conservation Laws, Spectral Deferred Corrections (SDC) Methods, Piecewise Parabolic Method (PPM), Godunov Methods, High Resolution Schemes

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.4, December 9, 2011

  ABSTRACT: We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge-averaged quantities, which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [1]. However, [1] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [1]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.