Assessing the performance of a three dimensional hybrid central-WENO finite difference scheme with computation of a sonic injector in supersonic cross flow

A hybridization of a high orderWENO-Z finite difference scheme and a high order central finite differencemethod for computation of the two-dimensional Euler equations first presented in [B. Costa andW. S. Don, J. Comput. Appl. Math., 204(2) (2007)] is extended to three-dimensions and for parallel computation. The Hybrid scheme switches dynamically from aWENO-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 expensiveWENO-Z scheme for highresolution capturing of shocks, whereas the remainder of grid pointsmay 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 aWENO-Z scheme only for the sonic injector benchmark.