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, 2021)
A hybridization of a high order WENO-Z finite difference scheme and a high ordercentral finite difference method for computation of the two-dimensional Eulerequations 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 schemeswitches dynamically from a WENO-Z scheme to a central scheme at any grid locationand time instance if the flow is sufficiently smooth and vice versa if the flow isexhibiting sharp shock-type phenomena.  The smoothness of the flow is determined bya high order multi-resolution analysis.  The method is tested on a benchmark sonicflow injection in supersonic cross flow.  Increase of the order of the method reducesthe numerical dissipation of the underlying schemes, which is shown to improve theresolution of small dynamic vortical scales.  Shocks are captured sharply in anessentially 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 Hybridscheme are in very close agreement.  Thirty percent of grid points require acomputationally expensive WENO-Z scheme for high-resolution capturing of shocks,whereas the remainder of grid points may be solved with the computationally moreaffordable central scheme.  The computational cost of the Hybrid scheme can be upto a factor of one and a half lower as compared to computations with a WENO-Z schemeonly for the sonic injector benchmark.