Under-Resolved DNS of Non-trivial Turbulent Boundary Layers via Spectral/hp CG Schemes

Abstract

This study assesses the suitability of spectral/hp continuous Galerkin (CG) schemes [1] for model-free under-resolved simulations of a non-trivial turbulent boundary layer flow. We consider a model problem proposed by Spalart in [2] that features a rotating free-stream velocity and admits an asymptotic solution with significant crossflow effects. Note this test case is substantially more complex than typical turbulent boundary layer canonical problems owing to its unsteadiness and enhanced small-scale anisotropy. Reported LES-based solutions to this problem are known to require sophisticated modelling and relatively fine grids to achieve meaningful results, with traditional models exhibiting poor performance. The model-free CG-based approach advocated, on the other hand, yields surprisingly good results with considerably less degrees of freedom for higher order discretisations. Usefully accurate results for the mean flow quantities could even be obtained with half as many degrees of freedom per direction (in comparison to reference LES solutions). Usage of high-order spectral element methods (CG in particular) is therefore strongly motivated for wall-bounded turbulence simulations via under-resolved DNS (uDNS), sometimes called implicit LES (iLES), approaches.