STABLE AND TIME-DISSIPATIVE FINITE-ELEMENT METHODS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN ADVECTION DOMINATED FLOWS

This paper examines a new Galerkin method with scaled bubble functions which replicates the exact artificial diffusion methods in the case o f I-D scalar advection-diffusion and that leads to non-oscillatory sol utions; as the streamline upwinding algorithms for 2-D scalar advectio n-diffusion and incompressible Navier-Stokes. This method retains the satisfaction of the Babuska-Brezzi condition and, thus, leads to optim al performance in the incompressible limit: This method, when, combine d with the recently-proposed linear unconditionally stable algorithms of Simo and Armero (1993), yields a method for solution of the incompr essible Navier-Stokes equations ideal for either diffusive or advectio n-dominated flows. Examples from scalar advection-diffusion and the so lution of the incompressible Navier-Stokes equations are presented.