Developments in Mesh-Moving and Mesh-Update Schemes for Space-Time Finite Element Dicretisations of Fluid Flows

Space-time discretisations of physical problems involving moving and deforming bodies, boundaries and interfaces have been shown to offer advantageous properties, while being methodologically uniform and flexible. Well-known phenomena, which are ideally suited to be analysed by space-time methods, are fluid-structure interaction problems in general as well as fluid flows with subdomain phase boundaries or immersed moving objects.
In this contribution existing mesh-moving and mesh-update techniques are comparatively discussed within the framework of finite element discretisations of the Navier-Stokes equations in space and time. The investigation is based on a SUPG/PSPG velocity-pressure formulation on the deforming space-time do- main.
Developments of mesh reconnection at fluid-solid interfaces due to mesh-moving/reconnecting proce- dures for space-time discretisations of fluid flows are presented. Furthermore mesh-update/reconnecting techniques are examined occurring in engineering problems involving sliding or rotating space-time fluid meshes.
The presented techniques are accompanied by numerical examples of translational fluid flow as well as fluid flow with immersed rotating fluid bodies. The quality of the approximative solution on the moving and deforming mesh as well as its conservation properties are investigated.