Stabilized and Galerkin Least Squares Formulations

We study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving problems as opposed to div-stable pairs used earlier. Higher order spectral/hp approximations are utilized for solving two dimensional computational fluid dynamics (CFD) problems with the new formulations named as the augmented SUPS (ASUPS) and augmented Galerkin Least Squares (AGLS) formulations. Excellent conservation of mass properties are observed for the problem with open boundaries in confined enclosures. Inexact Newton Krylov methods are used as the non-linear solvers of choice for the problems studied. Faithful representations of all fields of interest are obtained for the problems tested.