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

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

Year:    2012

Author:    Wai-Sun Don, Antonio de Gregorio, Jean-Piero Suarez, Gustaaf B. Jacobs

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 719–736

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-12S03

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 719–736

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Weighted essentially non-oscillatory central difference multi-resolution hybrid shock injector.

Author Details

Wai-Sun Don

Antonio de Gregorio

Jean-Piero Suarez

Gustaaf B. Jacobs

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