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Implicit meanflow-multigrid algorithms for Reynolds stress model computation of 3-D anisotropy-driven and compressible flows. (English) Zbl 1421.76170
Summary: The present paper investigates the multigrid (MG) acceleration of compressible Reynolds-averaged Navier-Stokes computations using Reynolds-stress model 7-equation turbulence closures, as well as lower-level 2-equation models. The basic single-grid SG algorithm combines upwind-biased discretization with a subiterative local-dual-time-stepping time-integration procedure. MG acceleration, using characteristic MG restriction and prolongation operators, is applied on meanflow variables only (MF-MG), turbulence variables being simply injected onto coarser grids. A previously developed non-time-consistent (for steady flows) full-approximation-multigrid (s-MG) is assessed for 3-D anisotropy-driven and/or separated flows, which are dominated by the convergence of turbulence variables. Even for these difficult test cases CPU-speed-ups $$r_{\text{CPUSUP}}$$[3, 5] are obtained. Alternative, potentially time-consistent approaches (unsteady u-MG), where MG acceleration is applied at each subiteration, are also examined, using different subiterative strategies, MG cycles, and turbulence models. For 2-D shock wave/turbulent boundary layer interaction, the fastest s-MG approach, with a V(2, 0) sawtooth cycle, systematically yields CPU-speed-ups of $$5\pm \frac 12$$, quasi-independent of the particular turbulence closure used.

##### MSC:
 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76N15 Gas dynamics (general theory) 35Q30 Navier-Stokes equations 76F40 Turbulent boundary layers 76L05 Shock waves and blast waves in fluid mechanics
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