THE CHARACTERISTIC STREAMLINE DIFFUSION METHOD FOR THE TIME-DEPENDENT INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

The paper presents a streamline diffusion finite element method for time-dependent flow problems, with or without free surface, governed by the incompressible Navier-Stokes equations. The method is based on space-time elements, discontinuous in time and continuous in space, which yields a general setting: if the elements are oriented along the characteristic direction in space-time a Lagrangian method is obtained, if they are fixed the method is Eulerian. Thus the method may be implemented as an arbitrary Lagrangian-Eulerian method, retaining the advantages of the streamline diffusion method on fixed grids. In particular. our method is stable in the whole range of Reynolds numbers and yields the possibility of equal order interpolation for velocity and pressure. Furthermore, since the solution is allowed to be discontinuous in time at discrete time levels, large deformations of the original domain are easily handled, e.g. with remeshing. Numerical results for some 2D-problems are given.