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Finite element implementation of boundary conditions for the pressure Poisson equation of incompressible flow
Author(s) -
Hassanzadeh Siamak,
Sonnad Vijay,
Foresti Stefano
Publication year - 1994
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.1650181102
Subject(s) - finite element method , pressure correction method , mathematics , neumann boundary condition , poisson's equation , compressibility , boundary value problem , galerkin method , incompressible flow , flow (mathematics) , mathematical analysis , boundary element method , reynolds number , geometry , mechanics , physics , turbulence , thermodynamics
In this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that the direct Galerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier‐Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requires C 1 continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventional C 0 elements. Numerical results using this approach for a wall‐driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two‐dimensional problem using the p ‐version of the finite element method, the approach presented here is general and remains valid for the conventional h ‐version as well as three‐dimensional problems.