A SPACE-TIME GALERKIN LEAST-SQUARES FINITE-ELEMENT FORMULATION OF THENAVIER-STOKES EQUATIONS FOR MOVING DOMAIN PROBLEMS/

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 int erfaces. The variational equation is based on the time discontinuous G alerkin method employing the physical entropy variables. The space-tim e elements are oriented in time to accommodate the spatial deformation s. If the elements are oriented along the particle paths, the formulat ion is Lagrangian and if they are fixed in time, it is Eulerian. Conse quently this formulation is analogous to the arbitrary Lagrangian-Eule rian (ALE) technique. A novel mesh rezoning strategy is presented to o rient the elements in time and adapt the fluid mesh to the changing sp atial configuration. Numerical results are presented to show the perfo rmance of the method.