In this work we develop an automatic dissipation/dispersion algorithm (ADDA) for high-order finite-volume methods on unstructured meshes, by extending the previous developed technique [1,2]. For very high-order finite-volume methods in under-resolved settings the dissipation provided by the numerical scheme might not be suitable to provide the correct energy transfer across scales, while at the same time the presence of dispersion might contaminate the solution with oscillations. The energy ratio of (as defined in [1,2]) is used as the key indicator for the tuning of the ADDA algorithm, which is tuned through the linear weight values of the central stencils of a CWENO/CWENOZ type of schemes [3]. The development and implementation is performed in the open-source CFD solver UCNS3D [4] (www.ucns3d.com) and a series of challenging test problems have been used to calibrate and assess the performance of the developed ADDA mechanism, including the subsonic and supersonic Taylor-Green vortex flow problem, isotropic turbulence decay. The algorithm developed can be a key component in establishing a more robust framework for high-order finite-volume methods for unresolved DNS, and implicit or explicit LES settings for practical flows of high-Reynolds number of complicated geometries.