Space-time shear-slip mesh update method for fluid-structure interaction problems

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 a short overview of existing mesh- moving techniques is given within the framework of finite element discretisations of the incompressible Navier-Stokes equations in space and time. The investigation is based on a velocity-pressure formulation on the deforming space-time domain in combination with a GLS stabilisation of the balance of momentum as well as the conservation equation of mass. A modification of the shear-slip mesh update method in the framework of space-time finite element discretisation is presented leading to a continuous space-time mesh in the shear-slip layer. The modified mesh moving technique is applied to the classical flow situation of Poiseuille flow incorporating a rotating space-time fluid mesh. Its conservation properties and its quality regarding the approximated solution on moving and deforming meshes are investigated.