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Invariant discretization of the incompressible Navier‐Stokes equations in boundary fitted co‐ordinates
Author(s) -
Segal A.,
Wesseling P.,
Van Kan J.,
Oosterlee C. W.,
Kassels K.
Publication year - 1992
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/fld.1650150404
Subject(s) - discretization , mathematics , curvilinear coordinates , mathematical analysis , navier–stokes equations , pressure correction method , boundary value problem , incompressible flow , compressibility , invariant (physics) , geometry , flow (mathematics) , physics , mechanics , mathematical physics
The discretization of the incompressible Navier‐Stokes equation on boundary‐fitted curvilinear grids is considered. The discretization is based on a staggered grid arrangement and the Navier‐;Stokes equations in tensor formulation including Christoffel symbols. It is shown that discretization accuracy is much enhanced by choosing the velocity variables in a special way. The time‐dependent equations are solved by a pressure‐correction method in combination with a GMRES method. Special attention is paid to the discretization of several types of boundary conditions. It is shown that fairly non‐smooth grids may be used using our approach.