| A space-time finite element formulation of the Navier-Stokes equations is presented for the analysis of fluid-structure interaction problems. The variational equation is based on time discontinuous Galerkin method employing the physical entropy variables. The space-time elements can be oriented in time to accommodate the spatial deformations. If the elements are oriented along the particle paths, the method is Lagrangian and if they are fixed in time, it is Eulerian. Consequently this formulation has the essence of the arbitrary Lagrangian-Eulerian techniques. Exploiting the idea of arbitrary orientation of the space time elements, a novel mesh rezoning technique is proposed to adapt the fluid mesh to the moving domain. The technique is entirely general in that it can effectively be applied to structured and unstructured meshes, thus allowing more kinematically complex problems to be handled effectively. The structural subdomain is modeled via elasticity elements with in-plane rotational degrees of freedom. The underlying variational formulations are shown to be convergent for all displacement rotation combinations. Technical issues involved in the coupling of fluid and solid subdomains are addressed and numerical results are presented to show the performance of the method. |
