A new formulation for scale-resolved simulations of turbulence with variable resolution (VR) is proposed. A delayed detached-eddy simulation (DDES) model based on the \(k-\omega\) framework is extended with VR-terms representing the commutation terms arising from variable resolution defined in terms of the DDES length scale. The VR-terms are responsible for the exchange of turbulence kinetic energy between the resolved and unresolved partitioning of the computational representation of turbulent flow. The new formulation is implemented in a general-purpose CFD code and applied on two cases, namely, a mixing shear layer and a wall-mounted hump and have been compared with and combined with the baseline model and two additional grey-area mitigation (GAM) formulations. The proposed method is shown to provide the mechanism for the exchange of energy between unresolved and resolved representation of the flow and to enhance the transition from modelled to resolved turbulence and thus improve the prediction of the resolved Reynolds stresses, development of the vorticity thickness for the shear layer flow and the skin friction recovery length for the hump flow.
