Augmented Stabilized Formulations with Fictitious Boundary Methods

Augmentation of the SUPS formulation was introduced earlier and successfully applied to solving incompressible NavierStokes equations for both two dimensional and three dimensional problems. Fictitious boundary methods (FBM) is a new methodology that aid the study of flow descriptions around solid obstacles on fixed Cartesian product grids that do not require body confirming meshes. FBM has been applied to lower order finite element and spectral/hp least squares techniques. We test the augmented stabilized finite element formulation introduced earlier, (ASUPS) to the fictitious boundary context and use it to solve incompressible flow problems. Utilizing the advantages of fictitious boundary methods we present solutions to flow around an array of two dimensional and three dimensional problems. In two dimensional flow computations we solve flow past a circular and elliptical shaped cylinders. For the ellipse shaped obstacles in a Newtonian flow field we examine the effects of varying boundary conditions and aspect ratios on the flow metrics. Finally we extend the procedures to solving two ellipse and two circular shaped obstacles facing the free stream. In three dimensional computations we examine incompressible flow around a three dimensional ellipse shaped obstacle at Reynolds number Re-200.