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On the accuracy and robustness of implicit LES / under-resolved DNS approaches based on spectral element methods

Rodrigo C. Moura
Department of Aeronautics, Imperial College London Prince Consort Rd, London, SW7 2BY, UK

Joaquim Peiro
Department of Aeronautics, Imperial College London Prince Consort Rd, London, SW7 2BY, UK

Spencer J. Sherwin
Department of Aeronautics, Imperial College London, Prince Consort Rd, London, SW7 2BY, UK

Abstract

We present a study on the suitability of under-resolved DNS (uDNS) − also called implicit LES (iLES) − approaches based on spectral element methods (SEM), with emphasis on high-order continuous and discontinuous Galerkin (i.e. CG and DG) schemes. Broadly speaking, these are model-free eddy-resolving approaches to turbulence which solve the governing equations in unfiltered form and rely on numerical stabilization techniques for small-scale regularization. Model problems in 1D, 2D and 3D are used in the assessment of solution quality and numerical stability. A rationale for the excellent potential of these methods for transitional and turbulent flows is offered on the basis of linear dispersion-diffusion analysis.