STREAM FUNCTION VORTICITY SOLUTION USING HIGH-P ELEMENT-BY-ELEMENT TECHNIQUES

A p-type finite-element scheme is introduced for Navier-Stokes problem s in a fully coupled stream function/vorticity formulation. The result ing coupled non-linear system is solved using a Newton iteration with incremental continuation in the Reynold's number. A biconjugate gradie nt (BCG) scheme in an element-by-element setting is applied to solve t he linearized system at each Newton iteration. Pseudo-element block pr econditioners produce a practical PBCG method, even for ill-conditione d systems arising from high-p elements in the case of Stokes flow. The problem at higher Reynolds numbers further limits p.