A Comparison of Linear and Nonlinear Finite Element Stabilization Techniques for Fluid Problems

Sammanfattning: The standard Galerkin, entropy viscosity (EV) and streamline upwind Petrov Galerkin (SUPG) methods were implemented for the advection equation and the Navier-Stokes equations for an incompressible fluid to determine which of the methods is better in terms of accuracy and time requirements. For the advection equation a disk with a rotating stream was modeled for both a continuous and a discontinuous initial condition. For both cases the SUPG method wins in all categories and seems to keep doing it for an infinite refinement of the mesh. The second best results are produced by the EV method in both of the categories for both test cases and the worst method turns out to be the standard Galerkin method. As for the Navier-Stokes equations two kinematic viscosity cases were tested, one with a relatively low viscosity and one with a higher viscosity corresponding to a benchmark computation. The system in consideration was a wind tunnel topology with a cylindrical object in the flow. For the higher kinematic viscosity study the standard Galerkin method seems to be the better choice with the EV method coming in second place. The SUPG method starts showing off substantial time requirements with no or less gain in accuracy. As for the low kinematic viscosity study the standard Galerkin method exhibits unstable behavior and gives unreasonably high velocities for most simulations, hence showing off the need for stabilization techniques. The EV method once again is the faster method for the simulation but no conclusion regarding which method yields the most accurate results can be made. Both methods yield the expected physical results with von Karman vortices forming and traveling down stream.