Finite element stream function‐vorticity solutions of the incompressible Navier‐Stokes equations
- 1 January 1987
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Fluids
- Vol. 7 (1) , 17-27
- https://doi.org/10.1002/fld.1650070103
Abstract
The incompressible, two‐dimensional Navier‐Stokes equations are solved by the finite element method (FEM) using a novel stream function/vorticity formulation. The no‐slip solid walls boundary condition is applied by taking advantage of the simple implementation of natural boundary conditions in the FEM, eliminating the need for an iterative evaluation of wall vorticity formulae. In addition, with the proper choice of elements, a stable scheme is constructed allowing convergence to be achieved for all Reynolds numbers, from creeping to inviscid flow, without the traditional need for upwinding and its associated false diffusion. Solutions are presented for a variety of geometries.Keywords
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