Space-Time Shear-Slip Mesh Update Method for Fluid-Structure Interaction Problems

Many practical problems in engineering consist of a structure surrounded by a fluid. These are all from the theoretical point of view fluid-structure interaction problems, in which the movement of the structure influences the flow field of the fluid and vice versa.
In this contribution the structure is described in a total Lagrangian representation based on velocities and the 2nd Piola-Kirchhoff stress state as primal variables in a hybrid-mixed formulation, while the fluid is modelled via the incompressible Navier-Stokes equations with velocities and pressure as unknowns.
The governing equations of fluid and structural dynamics are uniformly discretised using space-time finite elements [1]. The discretised model equations of the fluid are stabilised using a SUPG/PSPG approach. Shape and test functions are continuous within the space-time slabs, while across the space- time slabs the shape and test functions are continuous only in space, but discontinuous in time yielding a time-discontinuous Galerkin approach. The space-time discretisation of the coupled system with velocities and pressure as remaining unknowns lays the basis for a mathematically profound analysis due to its methodical uniformity.
During the mesh generation of the fluid-structure problem a fitting mesh at the conjoint interface of fluid and structure is generated ensuring natively the geometric continuity. In the discretised flow domain, which model equations are formulated in the Eulerian framework, a mesh-moving scheme needs to be applied to avoid severe mesh distortions. In case of large but regular structural displacements a discontinuous mesh-moving scheme like the Shear-Slip Mesh Update Method (SSMUM) is applicable [2].
In order to increase robustness and conservation behaviour of the classical SSMUM a modification based on the space-time discretisation of the problem described above is investigated. In the Space- Time SSMUM (ST-SSMUM) the alteration of the spatial connectivity takes place continuously in the space-time domain. By avoiding sudden changes in the spatial connectivity between two adjacent space-time slabs any difficulty in evaluating the jump term is circumvented.
The properties of the introduced ST-SSMUM is shown by a computation of the flow field of a rotating impeller, which can be interpreted as a simplified water turbine or blood pump.