Three-dimensional incompressible Navier–Stokes equations on non-orthogonal staggered grids using the velocity–vorticity formulation

✍ Scribed by F. Bertagnolio; O. Daube

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 665 KB
• Volume: 28
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19981030)28:6<917::aid-fld751>3.0.co;2-p

✦ Synopsis

This paper is concerned with the numerical resolution of the incompressible Navier -Stokes equations in the velocity-vorticity form on non-orthogonal structured grids. The discretization is performed in such a way, that the discrete operators mimic the properties of the continuous ones. This allows the discrete equivalence between the primitive and velocity-vorticity formulations to be proved. This last formulation can thus be seen as a particular technique for solving the primitive equations. The difficulty associated with non-simply connected computational domains and with the implementation of the boundary conditions are discussed. One of the main drawback of the velocity -vorticity formulation, relative to the additional computational work required for solving the additional unknowns, is alleviated. Two-and three-dimensional numerical test cases validate the proposed method.