In this work we use an implementation of the Discontinuous Galerkin (DG) method which features on-the-fly adaptive mesh refinement for unstructured hybrid meshes for the modelling of cavitating two-phase flows. The specific implementation has been developed for the resolution of complex multiscale phenomena, where high accuracy p-adaptive discretisations are combined with an h-adaptive data structure. The suggested approach accommodates the fine spatial resolution of the interface discontinuities in a cavitating flow.The physical problem of a cavitating flow is modelled by the simple barotropic model, as a unified compressible working fluid. The governing equations consist of the transport equations for the conservation of mass and momen-tum. Pressure, is calculated explicitly from the density distribution using the a piece-wise equation of state (EoS).The Tait EoS is used for the saturated liquid and an isentropic approximation is used for evaluation of the vapour-liquid mixture pressure. Scope of this work is to obtain a high order discretisation for the conservation of mass and momentum, to accurately describe the the flow structures responsible for the formation of cavitation bubbles, andalso the capturing of the resulting shocks during bubble collapse.The numerical approach is assessed for a series of test cases of compressible two-phase flows. Specifically, theone-dimensional shock tube problem for the advancement of a compressible interface front and the symmetric bub-ble collapse problem are considered. Furthermore, the axisymmetric bubble collapse near a wall is also presented.The method is applied for the Large Eddy Simulation (LES) in a micro-channel flow used for the study of the effectsof cavitation on liquid jet atomisation.