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.

提出了一种基于不连续Galerkin方法（DG）的高阶自适应网格细化（AMR）方法对空化流建模的方法。AMR实施使用了针对非结构化混合网格的动态自适应网格细化功能。已经开发出用于解决复杂的多尺度现象的特定实现方式，其中高精度的p自适应离散化与h自适应数据结构相结合。这种方法为界面不连续性和可压缩空化流中观察到的冲击波提供了良好的空间分辨率。泰特状态方程用于液相建模，而液/蒸气混合物则假定为等熵路径。为了解决质量和动量守恒方程的积分问题，使用了二阶空间和三阶非振荡时间离散化方法，以便解决造成空化气泡和压缩波形成的流动结构。对可压缩的液-气界面的一维推进和球形气泡的对称塌陷进行了开发方法的评估。

随后，利用已开发的多尺度建模AMR方法获得的结果表明，在刚性壁附近存在复杂的气泡坍塌机制，为以前的过程由于降低的分辨率和过去模拟的耗散性而未知提供了证据。发现伴随着气泡在壁附近破裂的撞击射流引起涡旋结构，这导致在撞击射流剪切层附近形成附壁泡沫的二次空化。在初始气泡破裂的最后阶段，发现撞击射流穿透壁泡的中心线，导致其部分破裂。这种次级塌陷导致冲击波具有丰富的空间结构，并与次级气泡相互作用。此外，