A comparison of higher-order finite-difference shock capturing schemes. (20th November 2015)

• Record Type: Journal Article
• Authors: Brehm, Christoph; Barad, Michael F.; Housman, Jeffrey A.; Kiris, Cetin C.
• Is Part Of: Computers & fluids. Volume 122(2015)
• Page Start: 184
• Page End: 208
• Publication Date: 2015-11-20
• Subjects: Higher order -- Shock capturing -- Finite difference -- WENO -- Localized artificial diffusivity -- Artificial dissipation; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2015.08.023
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Comparison of three most common classes of higher-order finite difference shock capturing schemes. Truncation error and spectral resolution analysis of the underlying optimal schemes. Wide range of test cases were used to study key aspects of higher-order schemes. Detailed cost breakdown of each individual scheme. Comparison of the overall cost and efficiency of the different schemes. Abstract: 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.