A method for solving the factorized vorticity-stream function equations by finite elements

✍ Scribed by L. Quartapelle; M. Napolitano

• Publisher: John Wiley and Sons
• Year: 1984
• Tongue: English
• Weight: 826 KB
• Volume: 4
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650040202

✦ Synopsis

A new finite element method for solving the time-dependent incompressible Navier-Stokes equations with general boundary conditions is presented. The two second-order partial differential equations for the vorticity and the stream function are factorized, apart from the non-linear advection term, by eliminating the coupling due to the double spccification on the stream function at (a part of) the boundary. This is achieved by reducing the no-slip boundary conditions to projection integral conditions for the vorticity field and by evaluating the relevant quantities involved according 10 an extension of the method of Glowinski and Pironneau for the biharmonic problem. Time integration schemes and iterative algorithms are introduced which require the solution only of banded linear systems of symmetric type. The proposed finite element formulation is compared with its finite diSference equivalent by means o f a few numerical examples. The results obtained using 4-noded bilinear elements provide an illustration of the superiority of the finite element based spatial discretization. KI'Y WORDS Finite elements wavier-Stokes Vorticity-stream function Time-dependent flows Boundary conditions Incompressible viscous flows Two-dimensional flows