A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems Original Research Article

A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations is presented for the analysis of free surface flows, moving spatial configurations and deforming fluid-structure interfaces. The variational equation is based on the time discontinuous Galerkin method employing the physical entropy variables. The space-time elements are oriented in time to accommodate the spatial deformations. If the elements are oriented along the particle paths, the formulation is Lagrangian and if they are fixed in time, it is Eulerian. Consequently this formulation is analogous to the arbitrary Lagrangian-Eulerian (ALE) technique. A novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration. Numerical results are presented to show the performance of the method.