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A 3D incompressible Navier-Stokes velocity-vorticity weak form finite element algorithm. (English) Zbl 1009.76059

Summary: The velocity-vorticity formulation is selected to develop a time-accurate CFD finite element algorithm for 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 no-slip wall boundary condition which also enforces the incompressibility constraint. We use a biconjugate gradient stabilized (BiCGSTAB) sparse iterative solver to solve the fully coupled system of equations by 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 obtained and compared with available benchmark solutions.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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