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....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 shockcapturing 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 highresolution 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.展开更多
基金We would like to acknowledge the funding support of this research by the RGC grant HKBU-200910 from Hong Kong University Grant Council(Don)an AFOSR-Young Investigator Grant(AFOSR-F9550-09-1-0097)+1 种基金the support by NSF(NSF-DMS-1115705)the Computational Science Research Center at SDSU(Jacobs).We further extend our gratitude to Prof.Parra at the University of Valladolid for her efforts in the exchange program of students between the University of Valladolid and San Diego State University.
文摘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 shockcapturing 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 highresolution 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.
