A 3D incompressible Navier-Stokes velocity-vorticity weak form finite element algorithm

The velocity-vorticity formulation is selected to develop a time-accurate CFD finite element algorithm for the incompressible Navier-Stokes equations in three dimensions. The finite element implementation uses equal order trilinear finite elements on a non-staggered hexahedral mesh. A second order vorticity kinematic boundary condition is derived for the no slip wall boundary condition which also enforces the incompressibility constraint. A biconjugate gradient stabilized (BiCGSTAB) sparse iterative solver is utilized to solve the fully coupled system of equations as a Newton algorithm. The solver yields an efficient parallel solution algorithm on distributed-memory machines, such as the IBM SP2. Three dimensional laminar flow solutions for a square channel. a lid-driven cavity, and a thermal cavity are established and compared with available benchmark solutions. Copyright 0 2002 John Wiley Sons, Ltd.