Abstract

In this paper we develop a family of arbitrarily high-order non-oscillatory hybrid Finite Volume/Discontinuous Galerkin schemes for turbulent flows on mixed-element unstructured meshes. The schemes are inherently compact in the sense that the central stencils employed are as compact as possible, and that the directional stencils are reduced in size, simplifying their implementation. Their key ingredient is the switch between a DG method and a FV method based on the CWENOZ scheme when a troubled cell is detected. Therefore, in smooth regions of the computational domain, the high order of accuracy offered by DG is preserved, while in regions with sharp gradients, the robustness of FV is utilized. This paper also presents the time evolution of troubled cells in unsteady test cases and the use of extended bounds for troubled cell detection. We assess the performance of these schemes in terms of accuracy, robustness and computational cost through a series of stringent 2D and 3D test problems. The results obtained demonstrate the accuracy and robustness that the schemes offer and highlight areas of future improvements that are considered.

Abstract

We perform Large Eddy Simulation on a 3D NACA0012 airfoil using a high order discontiuous Galerkin spectral element solver at moderate Reynolds numbers, Re = 1.0 · 105. The aim is to compare the results of classic explicit Sub Grid Scale models, e.g. the WALE and VREMAN models, with the ones get by using implicit LES, where no explicit SGS is used, but we use stabilising split-form energy-stable formulations, with two-point Pirozzoli and KennedyGruber fluxes. We compare general qualitative variables such as the Q-criteria as well as local quantitative variables, as boundary layer velocity profiles. We show that both methods achive similar predictions for the integrated global variables, but differences can be appreciated in the local velocity profiles.