Application of wall-models to discontinuous Galerkin LES

Frère, Ariane [UCL] Carton de Wiart, Corentin [NASA] Hillewaert, Koen [Cenaero] Chatelain, Philippe [UCL] Winckelmans, Grégoire [UCL]

Wall-resolved LES are still limited to moderate Reynolds number flows due to the high computational cost required to capture the inner part of the boundary layer. Wall-modeled LES (WMLES) provide more affordable LES by modeling the near-wall layer. Wall function-based WMLES solve LES equations up to the wall, where the coarse mesh resolution essentially renders the calculation under-resolved. This makes the accuracy of WMLES very sensitive to the behavior of the numer- ical method. Therefore, best practice rules regarding the use and implementation of WMLES cannot be directly transferred from one methodology to another re- gardless of the type of discretization approach. Whilst numerous studies present guidelines on the use of WMLES, there is a lack of knowledge for discontinuous fi- nite element-like high-order methods. Incidentally, these methods are increasingly used on the account of their high accuracy on unstructured meshes and their strong computational efficiency. The present paper proposes best practice guidelines for the use of WMLES in these methods. The study is based upon sensitivity analyses of turbulent channel flow simulations by means of a Discontinuous Galerkin approach. It appears that good results can be obtained without the use of a spatial or temporal averaging. The study confirms the importance of the wall function input data location and suggests to take it at the bottom of the second off-wall element. This data being available through the ghost element, the suggested method prevents the loss of computational scalability experienced in unstructured WMLES. The study also highlights the influence of the polynomial degree used in the wall-adjacent element. It should preferably be of even degree as using polynomials of degree two in the first off-wall element provides, surprisingly, better results than using polynomials of degree three.