Optimized Filters for Stabilizing High-Order Large Eddy Simulation
Mohsen Hamedi, Brian C. Vermeire
Abstract
High-order Flux Reconstruction (FR) schemes can be used to simulate unsteady turbulent flows using Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) in the vicinity of complex geometries. However, the application of FR can be limited by non-linear instabilities, which can arise from oscillatory behaviour of the underlying polynomial representation of the solution. In this paper, we explore filtering and its parametrization for stabilizing under-resolved simulations of the Navier–Stokes equations. A new exponential filtering operator is proposed, which is normalized by the time-step size and designed to filter high-frequency modes. Over 14,000 numerical tests are then performed to obtain an optimal set of filtering parameters, with the objective being to stabilize while maintaining high-order accuracy. We then verify that these optimal filters converge to super-accuracy for non-linear problems, and compare filtered and unfiltered simulations of the Taylor–Green vortex using both straight and curved meshes, and turbulent channel flow. These demonstrate that the filtered solutions are generally more accurate than unfiltered ones, while still stabilizing previously unstable simulations. Finally, we demonstrate the utility of these filters for more complex flows, specifically a stalled NACA 0020 airfoil.