Volume 4, Issue 6
Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow

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

Adv. Appl. Math. Mech., 4 (2012), pp. 719-736.

Published online: 2012-12

Preview Full PDF 539 4545
Export citation
  • 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

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

  • AMS Subject Headings

65P30, 77Axx

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-4-719, author = {Wai-Sun Don , and Antonio de Gregorio , and Jean-Piero Suarez , and Jacobs , Gustaaf B.}, title = {Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-12S03}, url = {http://global-sci.org/intro/article_detail/aamm/145.html} }
TY - JOUR T1 - Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow AU - Wai-Sun Don , AU - Antonio de Gregorio , AU - Jean-Piero Suarez , AU - Jacobs , Gustaaf B. JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 719 EP - 736 PY - 2012 DA - 2012/12 SN - 4 DO - http://doi.org/10.4208/aamm.12-12S03 UR - https://global-sci.org/intro/article_detail/aamm/145.html KW - Weighted essentially non-oscillatory, central difference, multi-resolution, hybrid, shock, injector. AB -

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.

Wai-Sun Don, Antonio de Gregorio, Jean-Piero Suarez & Gustaaf B. Jacobs. (1970). Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow. Advances in Applied Mathematics and Mechanics. 4 (6). 719-736. doi:10.4208/aamm.12-12S03
Copy to clipboard
The citation has been copied to your clipboard