A multi-scale formulation for compressible turbulent flows suitable for general variational discretization techniques

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    Abstract

    Based on the recently introduced variational multi-scale (VMS) approach to large-eddy simulation (LES) as introduced in [T.J.R. Hughes, L. Mazzei, K.E. Jansen, Large eddy simulation and the variational multiscale method, Comput. Visual. Sci. 3 (2001) 47–59; S.S. Collis, Monitoring unresolved scales in multiscale turbulence modeling, Phys. Fluids 13 (6) (2001) 1800–1806], we present a VMS formulation which can be used in the simulation of compressible flows. Special attention is given to obtain a VMS formulation which is suitable for complex flow domains and general variational discretization techniques. A generalization of the Favre-averaging procedure is introduced such that the formulation resembles the Favre-filtered Navier–Stokes equations traditionally used in LES of compressible flow, and no explicit subgrid terms arise in the continuity equation. Also, we show that with the use of discretization methods other than Fourier-spectral methods the VMS-projection no longer commutes with differentiation. This results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to LES.
    Original languageUndefined
    Article number10.1016/j.cma.2006.12.005
    Pages (from-to)2863-2875
    Number of pages13
    JournalComputer methods in applied mechanics and engineering
    Volume196
    Issue number1/29-30
    DOIs
    Publication statusPublished - 2007

    Keywords

    • Discontinuous Galerkin finite element methods
    • Turbulence
    • Variational multi-scale method
    • Commutator errors
    • EWI-11583
    • METIS-245865
    • IR-62059
    • Large eddy simulation

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