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Three‐dimensional incompressible Navier–Stokes equations on non‐orthogonal staggered grids using the velocity–vorticity formulation
Author(s) -
Bertagnolio F.,
Daube O.
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19981030)28:6<917::aid-fld751>3.0.co;2-p
Subject(s) - vorticity , discretization , mathematics , navier–stokes equations , computational fluid dynamics , vorticity equation , mathematical analysis , pressure correction method , compressibility , vortex , physics , mechanics
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. © 1998 John Wiley & Sons, Ltd.