A comparative study of explicit and implicit Large Eddy simulations using a high-order discontinuous Galerkin solver: Application to a Formula 1 front wing

This paper explores two Large Eddy Simulation (LES) approaches within the framework of the high-order discontinuous Galerkin solver, Horses3D. The investigation focuses on an Inverted Multi-element Wing in Ground Effect (i.e. 2.5D Imperial Front Wing section) representing a Formula 1 front wing, and compares the strengths and limitations of the two LES methods. The explicit LES formulation relies on the Vreman model that adapts to laminar, transitional and turbulent regimes. The numerical formulation uses nodal basis functions and Gauss points. The implicit LES formulation does not require explicit turbulence modeling but relies in the discretization scheme. We use the Kennedy-Gruber kinetic energy preserving formulation to enhance stability in under-resolved simulations, since we recover the continuous properties such as energy conservation at a discrete level. This formulation employs Gauss-Lobatto points, which downgrades the accuracy of integration but allows for larger time steps in explicit time integration. We compare our results to Nektar++, by Slaughter et al. in Flow, Turbulence and Combustion 110, 917–944 (2023), showing that both LES techniques provide results that agree well with the reference values. The implicit LES shows to better capture transition and allows for larger time steps at a similar cost per iteration. We conclude that this implicit LES formulation is very attractive for complex simulations. • Discontinuous Galerkin discretization for LES on a Formula 1 front wing section. • Kinetic energy conserving scheme for implicit LES with the Kennedy-Gruber fluxes. • Comparison of explicit subgrid scale modeling with implicit LES method. • Application on an extruded section of the Imperial Front Wing.