Solution of cavitating compressible flows using Discontinuous Galerkin discretisation

A methodology for modelling cavitating flows using a high-order Adaptive Mesh Refinement (AMR) approach based on the Discontinuous Galerkin method (DG) is presented. The AMR implementation used features on-the-fly adaptive mesh refinement for unstructured hybrid meshes. The specific implementation has been developed for the resolution of complex multi-scale phenomena where high accuracy p-adaptive discretisations are combined with an h-adaptive data structure. This approach accommodates the fine spatial resolution for the interface discontinuities and the shock waves observed in compressible cavitating flows. The Tait equation of state is used for the modelling of the liquid phase while an isentropic path is assumed for the liquid/vapour mixture. Second order spatial and a third order non-oscillatory temporal discretisation are used for the integration of the mass and momentum conservation equations, in order to resolve the flow structures responsible for the formation of cavitation bubbles and the resulting compression waves. Assessment of the developed methodology is performed for the one-dimensional advancement of a compressible liquid-vapour interface and the symmetric collapse of a spherical vapour bubble. Following, results obtained with the developed multi-scale modelling AMR approach has revealed a complex bubble collapse mechanism near a rigid wall, providing evidence of processes that have been unknown before due to reduced resolution and dissipative nature of past simulations. The impinging jet accompanying the collapse of a bubble near a wall, was found to induce vortical structures, which result to the formation of a secondary cavitation of a wall-attached bubble at the vicinity of the impingement jet shear layer. At the final stages of the initial bubble collapse, the impinging jet was found to penetrate the centre-line of the wall bubble inducing its partial collapse. This secondary collapse results to a rich spatial structure of shock waves, interacting with the secondary bubbles. Moreover, the calculated pressure level are found to be much higher than those reported from previous methodologies. © 2020 Elsevier Inc.