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
