3D flow calculations with an A-L-E description using space-time finite elements

A space-time finite element method based on an arbitrary Lagrangian-Eulerian description is developed and implemented for the solution of Navier-Stokes equations for predicting the unsteady incompressible flows past arbitrary geometries. The governing equations are expressed in the fixed frame of reference wherein the terms related to grid motion are included. Superparametric space-time elements are used in discretization of the domain in which the finite elements are both allowed to move and deform. The code developed here is calibrated and tested on the flow about a drifting sphere. First, the unidirectionally drifting sphere is set to drift from a steady state at an initial Reynolds number of 1000. In addition, laminar flow about a drifting and falling sphere is studied, starting from the steady state at a Reynolds number of 10,000.