A Petrov-Galerkin Finite Element Formulation for Convection Dominated Flows

In this thesis, a new finite element formulation for convection dominated flows is developed. The basis of the formulation is the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes. When implemented as a consistent Petrov-Galerkin weighted residual method, it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods. The effectiveness of the streamline upwind/Petrov-Galerkin formulation for the linear advection diffusion equation is demonstrated with numerical examples. The formulation is extended to the treatment of the incompressible Navier-Stokes equations. An efficient implicit pressure/explicit velocity transient algorithm is developed which allows for several treatments of the incompressibility constraint and for multiple iterations within a time step. The algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a Reynolds number of 100.