A Comparison of Higher-Order Finite-Difference Shock Capturing Schemes

Speaker: Christoph Brehm, NASA Ames Research Center
August 19, 2014

Presentation

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 numerical higher-order shock capturing schemes are available in the literature. The desired numerical scheme should be free of spurious numerical oscillations across discontinuities and 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 presentation: (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 explicit and compact finite difference forms. Multiple variations of these methods were implemented and tested using a block-structured Cartesian mesh solver. This presentation assesses shock capturing capabilities as well as effects on the accuracy in smooth flow regions. A new set of boundary candidate stencils for an upwind-biased compact weighted essentially non-oscillatory scheme are proposed which offer improved accuracy and stability at block and/or domain boundaries. The variety of test cases range from canonical shock problems to homogeneous isotropic turbulence at a turbulent Mach number of 0.5 where shocklets are formed.

Biography

Christoph Brehm joined the Science & Technology Corporation (STC) / Applied Modeling and Simulation branch at NASA Ames in 2012. He has been working in the LAVA group with special emphasis on unsteady flows, e.g., launch environment flows, buffeting and acoustics. Recently, he started an effort in developing higher-order shock capturing schemes for ILES/LES with the LAVA framework. He received a B.S./M.S. equivalent degree at the University of Stuttgart (Germany) and a Ph.D. at the University of Arizona under the supervision of Professor H.F. Fasel working on active flow control, immersed boundary methods and transition research.

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