A comparison of higher-order finite-difference shock capturing schemes

Christoph Brehm, Michael F. Barad, Jeffrey A. Housman, Cetin C. Kiris

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


The efficiency of computational fluid dynamics simulations can be greatly enhanced by employing higher-order accurate numerical schemes which provide superior accuracy for a given cost. For unsteady turbulent flow simulations involving shocks, contacts, and/or material discontinuities, various higher-order shock capturing schemes are available in the literature. The desired numerical scheme should be free of spurious numerical oscillations across discontinuities and it should obtain higher-order accuracy in smooth flow regions in an efficient manner. Sufficient robustness is necessary for effectively utilizing these numerical methods in engineering and science applications. Three classes of higher-order shock capturing schemes are compared in this paper: (1) central finite-difference schemes with explicit artificial dissipation, (2) a compact centered finite-difference scheme with localized artificial diffusivity and (3) weighted essentially non-oscillatory schemes in both explicit and compact finite difference forms. Multiple variations of these methods were implemented and tested using a block-structured Cartesian mesh solver. The current paper assesses shock capturing capabilities as well as effects on the accuracy in smooth flow regions using a variety of test cases that range from canonical shock problems to homogeneous isotropic turbulence at a turbulent Mach number of 0.5 where shocklets are formed. Finally, a computational cost breakdown for each scheme is provided and the overall computational efficiency of the different schemes are compared to each other.

Original languageEnglish
Pages (from-to)184-208
Number of pages25
JournalComputers and Fluids
StatePublished - Nov 20 2015


  • Artificial dissipation
  • Finite difference
  • Higher order
  • Localized artificial diffusivity
  • Shock capturing
  • WENO

ASJC Scopus subject areas

  • Computer Science (all)
  • Engineering (all)


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