The periodic hills simulation case is a well-established benchmark case for Computational Fluid Dynamics (CFD) solvers due to its complex features derived from the separation of a turbulent flow from a curved surface. We study the case with the open-source implicit large eddy simulation (ILES) software Lethe. Lethe solves the incompressible Navier-Stokes equations by applying a continuous Galerkin Finite Element discretisation with Least-Squares stabilisation. It is built upon the well-established deal.II library. Through its deal.II heritage, Lethe is able to handle large meshes (>1B cells), supports dynamic mesh adaptation and is based on a solid C++ architecture.

The solver is validated by comparison of the results to experimental and computational data obtained for the flow over periodic hills at $Re=5600$. In addition, we study the effect of the time step, averaging time and global refinement, and experiment with high-order elements. Lethe is shown to perform well even when using meshes coarser and time steps larger than those typically used in periodic hills studies. For an optimised ILES simulation, the time step must be sufficiently small to capture the rapidly changing turbulent effects, but this is compromised by a greater number of iterations increasing the computational expense. The averaging time required to achieve statistical steadiness is discussed and the mesh itself is investigated to determine the spatial resolution required for accurate simulations. The greater understanding of the effect of simulation parameters on the periodic hills case provided by this study can guide the optimisation of other simulations and lead to a greater benefit being obtained from ILES solvers.

This is joint work with Laura Prieto Saavedra, Catherine Radburn and Audrey Collard-Daigneault. This work was supported by NSERC RGPIN-2020-04510 Discovery grant. The authors would also like to acknowledge technical support and computing time provided by Compute Canada and Calcul Québec.