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

TL;DR

The study investigates explicit LES with the Vreman SGS model and implicit LES using Kennedy–Gruber entropy-stable discretization within the high-order DG solver Horses3D for a simplified Formula 1 front wing. It demonstrates that both approaches reproduce reference data well, with iLES better capturing transition and enabling larger time steps at comparable cost. The comparison reveals strong agreement in averaged fields, surface pressure and shear, and wake statistics, while highlighting differences in near-wall resolution and TKE predictions due to mesh constraints. The results endorse implicit entropy-stable iLES as a robust and efficient option for complex automotive flows and underline the potential of high-order methods in industrial aerodynamic simulations.

Abstract

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 entropy stable formulation to enhance stability in under resolved simulations, since we recover the continuous properties such as entropy 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++ [1] 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.

Figures (19)

• Figure 1: Overview of the domain and the mesh used for the analysis using Horses3D. The refined region is where the section of the front wing and its wake are placed.
• Figure 2: Close view of the mesh in the region of the three elements of the geometry. The mesh comprises of $3^{rd}$ order curvilinearl hexahedral elements.
• Figure 3: $X^{+}$ and $Y^{+}$ values for the iLES simulations using Horses3D for ($\mathrm{\ref{['fig:yplus_wing1']}}$) the mainplane, ($\mathrm{\ref{['fig:yplus_wing2']}}$) the first flap and ($\mathrm{\ref{['fig:yplus_wing3']}}$) the second flap.
• Figure 4: $X^{+}$ and $Y^{+}$ values for the eLES simulations using Horses3D for ($\mathrm{\ref{['fig:yplus_wing1_vrm']}}$) the mainplane, ($\mathrm{\ref{['fig:yplus_wing2_vrm']}}$) the first flap and ($\mathrm{\ref{['fig:yplus_wing3_vrm']}}$) the second flap.
• Figure 5: Comparison of time-averaged velocity magnitude contours for the ($\mathrm{\ref{['fig:uvel_avg_Horses3D']}}$) iLES results, ($\mathrm{\ref{['fig:uvel_avg_vreman_Horses3D']}}$) the eLES results and for the ($\mathrm{\ref{['fig:uvel_avg_nektar']}}$) Nektar++ results. The white isolines indicate the regions of recirculating flow.