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Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference scheme with Computation of a Sonic Injector in Supersonic Cross Flow

Published online by Cambridge University Press:  03 June 2015

Wai-Sun Don ,
Antonio de Gregorio ,
Jean-Piero Suarez  and
Gustaaf B. Jacobs
Wai-Sun Don*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Antonio de Gregorio
Affiliation:
Department of Aerospace Engineering & Engineering Mechanics, San Diego State University, 5500 Campanile Drive San Diego, CA 92182, USA
Jean-Piero Suarez
Affiliation:
Department of Aerospace Engineering & Engineering Mechanics, San Diego State University, 5500 Campanile Drive San Diego, CA 92182, USA
Gustaaf B. Jacobs*
Affiliation:
Department of Aerospace Engineering & Engineering Mechanics, San Diego State University, 5500 Campanile Drive San Diego, CA 92182, USA
*
Corresponding author. Email: wsdon@hkbu.edu.hk
Email: gjacobs@mail.sdsu.edu
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Abstract

A hybridization of a high order WENO-Z finite difference scheme and a high order central finite difference method for computation of the two-dimensional Euler equations first presented in [B. Costa and W. S. Don, J. Comput. Appl. Math., 204(2) (2007)] is extended to three-dimensions and for parallel computation. The Hybrid scheme switches dynamically from a WENO-Z scheme to a central scheme at any grid location and time instance if the flow is sufficiently smooth and vice versa if the flow is exhibiting sharp shock-type phenomena. The smoothness of the flow is determined by a high order multi-resolution analysis. The method is tested on a benchmark sonic flow injection in supersonic cross flow. Increase of the order of the method reduces the numerical dissipation of the underlying schemes, which is shown to improve the resolution of small dynamic vortical scales. Shocks are captured sharply in an essentially non-oscillatory manner via the high order shock-capturing WENO-Z scheme. Computations of the injector flow with a WENO-Z scheme only and with the Hybrid scheme are in very close agreement. Thirty percent of grid points require a computationally expensive WENO-Z scheme for high-resolution capturing of shocks, whereas the remainder of grid points may be solved with the computationally more affordable central scheme. The computational cost of the Hybrid scheme can be up to a factor of one and a half lower as compared to computations with a WENO-Z scheme only for the sonic injector benchmark.

Keywords

65P3077AxxWeighted essentially non-oscillatory central differencemulti-resolutionhybridshockinjector
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 6 , December 2012 , pp. 719 - 736
Copyright
Copyright © Global-Science Press 2012

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