Arbitrary-order unstructured finite-volume methods for implicit large eddy simulation of turbulent flows with adaptive dissipation/dispersion adjustment (ADDA)

Abstract

Implicit Large Eddy simulation (iLES) has gained substantial popularity for modelling high-Reynolds-number turbulent flows, found across several engineering and scientific fields. iLES on a first read represents a simple, computationally efficient, and straightforward way to model turbulent flows. The numerical dissipation/dispersion errors of high-resolution high-order numerical schemes employed in this context, can mimic the effects of the unresolved flow scales, and therefore acting like a subgrid-scale model, most often successfully. The numerical dissipation and dispersion of high-resolution methods are intertwined and controlling them to obtain physically meaningful results in under-resolved grid settings of compressible flows is challenging due to the presence of discontinuities and smooth flow features simultaneously. A numerical method should have the right amount of dissipation/dispersion, such that it can avoid the unphysical “build-up” of energy in the high modes or excessive diffusion, since this will render the method unsuitable for iLES. Several elegant approaches to master this delicate balance have been presented in the literature, including polynomial de-aliasing, Riemann solver dissipation adjustment, and adaptive blending of central and upwind schemes. This work presents an adaptive dissipation/dispersion adjustment (ADDA) algorithm that determines a well-resolved and under-resolved region and adjusts the numerical dissipation/dispersion of a high-order CWENOZ scheme, followed by further adjusting the flux-dissipation term depending on the presence of discontinuities. Implemented within an arbitrary-order finite-volume framework for unstructured meshes in compressible flows, the ADDA algorithm is put to the test across a range of under-resolved iLES simulations encompassing subsonic, transonic, and supersonic regimes. The developed framework exhibits enhanced robustness and scale-resolving capabilities, all while achieving physically meaningful results in a computationally efficient manner. All the methods have been implemented and have been made available to the research community in the open-source UCNS3D CFD solver to accelerate the improvement of the methods.