Development of a multiscale LES model in the context of a modal discontinuous Galerkin method

Abstract This paper introduces a variational multiscale simulation (VMS) approach in the context of high-order discontinuous Galerkin (DG) discretizations. First, a new calibration of the Smagorinsky model parameter ( C S Δ ) is proposed in terms of the DG discretization (grid size, h , and polynomial order, p ) and the selected VMS scale partition. Second, an efficient and simple implementation of the VMS version of the Smagorinsky model is presented. The dissipation properties of the DG discretizations for different values of h and p are then analysed based on Taylor–Green vortex computations in the limit of inviscid flow. The low levels of dissipation found for high-order DG discretizations emphasize the suitability of this type of discretization for LES. The performance of the presented approach is demonstrated by comparing DG/VMS computations of the Taylor–Green vortex at R e = 3000 with a reference spectral DNS.

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