Abstract
Thepurposeofthiswork isthedevelopmentofanefe cientand robustimplicitmethodology fortheintegration of the three-dimensional compressible Favre ‐Reynolds-averaged Navier ‐Stokes equations with near-wall Reynoldsstressclosure.Thee vemean-e owandseventurbulencetransportequationsarediscretizedinspace,ona structured multiblock grid,using an O(¢x 3)e nitevolumeupwind-biased MUSCL schemewithVanLeere ux vectorsplitting and Van Albada limiters. Time integration is based on an implicit dual-time-stepping procedure with alternating direction implicit subiterations. A particular treatment of the approximate Jacobians used in the subiterations substantiallydiminishesthecomputing timerequirementsoftheimplicitphase,sothatthecomputationaloverhead of the Reynolds-stress seven-equation closure, compared to a two-equation closure, is less than 30% per iteration. For steady e ow computations local time steps are used, for both the subiterations and the time marching, with Courant‐Friedrichs‐Lewynumbersof O(10‐20)fortheO(1‐20)subiterationsneededand O(100‐500)forthetime marching. The robustness of the method is ensured by appropriate positivity, boundedness, and Reynolds-stress realizability constraints. The numerical method is illustrated by computing (and conducting numerical studies ) for a high subsonic (M » 0:7) three-dimensional e ow with large separation and for a transonic three-dimensional shock-wave/boundary-layer interaction.
Published Version
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