Finiteelement model in vorticity and current function for the numerical solution of the NavierStokes equations
Abstract
A numerical procedure for the integration of the incompressible NavierStokes equations, when expressed in terms of a stream function equation and a vorticity transport equation, is presented. This procedure comprises the variational formulation of the equations, the construction of the approximation spaces by the finite element method and the discretization via the Galerkin method. For the stationary problems, the system of nonlinear algebraic equations resulting from the discretization is solved by the NewtonRaphson algorithm. Finally, for the transient problems, the solution of the nonlinear ordinary differential equations resulting from the spatial discretization is accomplished through a CrankNicolson scheme.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1984
 Bibcode:
 1984STIN...8630109D
 Keywords:

 Finite Element Method;
 NavierStokes Equation;
 Viscous Flow;
 Vortices;
 Vorticity Equations;
 Algorithms;
 Calculus Of Variations;
 Fluid Mechanics and Heat Transfer