High-Order Implicit Large Eddy Simulation using Entropically Damped Artificial Compressibility

Abstract

Performing industrial scale incompressible Large Eddy Simulation (LES) remains particularly challenging due to computational cost limitations. Recently, the Entropically Damped Artificial Compressibility (EDAC) method was introduced, which does not require coupled global solves or pseudo-time stepping. Parallel to this, high-order unstructured methods, such as the Flux Reconstruction (FR) approach, have been proposed for Implicit LES (ILES) of compressible turbulent flows. This work presents EDAC with FR as an ILES framework for incompressible flows. Results from a Taylor–Green vortex, turbulent channel flow, and transitional and turbulent flow over an SD7003 airfoil demonstrate the approach is accurate and stable for solutions polynomials of degree ps≤4, while some instabilities were observed beyond this. Higher-order solutions were found to be significantly more accurate than their lower-order counterparts compared to reference direct numerical simulation, and had lower divergence error even with less strict incompressibility factors. These results demonstrate that combining EDAC with FR provides a simple, accurate, efficient, and stable framework for performing ILES of incompressible flows. Additionally, this fully explicit framework does not require coupled solvers, pseudo-time stepping, or explicit subgrid scale models.