Finite Element Solution of a Stream Function-Vorticity System and Its Application to the Navier Stokes Equations

Finite Element Solution of a Stream Function-Vorticity System and Its Application to the Navier Stokes Equations

The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results p...

A Stabilized Finite Element Method for Stream Function Vorticity Formulation of Navier-stokes Equations

We the solvability of the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations. We use the time discretization and the method of characteristics order one for solving a quasi-Stokes system that we discretize by a piecewise continuous finite element method. A stabilization technique is used to overcome the loss of optimal error estimate. Finally a parallel numeric...

Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation

The standard discretization of the Stokes and Navier-Stokes équations in vorticity and stream function formulation by affine finite éléments is known for its bad convergence. We present here a modified discretization, we prove that the convergence is improved and we establish a priori error estimâtes. Résumé. Il est bien connu que la discrétisation usuelle des équations de Stokes et de Navier-S...

A Finite Element Solution Algorithm for the Navier-stokes Equations

H2 solutions for the stream function and vorticity formulation of the Navier-Stokes equations

We show that the two dimensional Navier–Stokes equations in the stream function and vorticity form with nonhomogeneous boundary conditions have a unique solution with a stream function having two space derivatives. 2005 Published by Elsevier Inc.