A hybrid numerical scheme for a new formulation of delayed detached-eddy simulation (DDES) based on elliptic relaxation

Abstract

A new formulation of Delayed Detached-Eddy Simulation (DDES) based on the φ - f elliptic relaxation model has been derived and calibrated. A suitable correction function Ψ and a model constant CDDES have been formulated and validated using decaying isotropic turbulence (DIT). The model has been applied to a 2D wall-mounted hump at high-Reynolds number where it has shown promising improvements over the common SST-DDES model. The improved RANS modelling of the near-wall physics results in an improved prediction of the levels of turbulent Reynolds stresses which leads to a better approximation of the recirculation zone and flow physics. A hybrid numerical scheme has also been developed for use with DDES; this blends an upwind based scheme and a centred scheme based explicitly on the blending function of the DDES.