Efficient implementation of essentially non-oscillatory shock-capturing schemes, II

  • Authors:

  • Chi-Wang Shu;Stanley Osher

  • Affiliations:

  • Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA;Department of Mathematics, University of California, Los Angeles, California 90024-1555, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 1989

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Abstract

In this paper we extend our earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes. We provide a new simplified expression for the ENO construction procedure based again on numerical fluxes rather than cell-averages. We also consider two improvements which we label ENO-LLF (local Lax-Friedrichs) and ENO-Roe, which yield sharper shock transitions, improved overall accuracy, for lower computational cost than previous implementation of the ENO schemes. Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations. The implementation for nonlinear systems and multi-dimensions is given. Finally, many numerical examples, including a compressible shock turbulence interaction flow calculation, are presented.