Equivalence of u–p and ζ–ψ formulations of the time-dependent Navier–Stokes equations

✍ Scribed by J.-L. Guermond; L. Quartapelle

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 799 KB
• Volume: 18
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650180504

✦ Synopsis

Abstract

This paper deals with the non‐stationary incompressible Navier‐‐Stokes equations for two‐dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H^1^ for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.