Scale-Resolving Simulations with a Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Flow Solvers

Abstract

A new low-dissipation low-dispersion second-order scheme is applied to scale-resolving flow simulations using compressible and incompressible unstructured finite volume solvers. In wall-resolved and wall-modeled large-eddy simulations of the plane channel flow, the new scheme yields substantial improvements compared to the more dissipative/dispersive standard central scheme over a considerable range of Reynolds numbers. For general hybrid Reynolds-averaged Navier–Stokes/large-eddy simulations, a numerical blending approach is derived that uses a local sensor function to switch between the new scheme in the large-eddy simulation branch and the standard scheme in inviscid flow regions. After determining a suitable sensor formulation, the hybrid numerical scheme is applied to simulate a backward-facing step flow, for which satisfactory results and a reduced grid sensitivity are obtained. To demonstrate its potential in relevant aeronautical flows, the new scheme is successfully applied to hybrid Reynolds-averaged Navier–Stokes/large-eddy simulations of a three-element airfoil near stall and a rudimentary landing gear with massive flow separation.