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The dual variable method for finite element discretizations of Navier/Stokes equations
Author(s) -
Hall C. A.,
Peterson J. S.,
Porsching T. A.,
Sledge F. R.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210508
Subject(s) - mathematics , finite element method , discretization , quadrilateral , basis function , basis (linear algebra) , piecewise , mathematical analysis , mixed finite element method , piecewise linear function , geometry , physics , thermodynamics
The numerical solution of two‐dimensional, transient, incompressible Navier–Stokes problems is considered. The dual variable method, originally developed in the context of a finite difference discretization, is a technique to considerably reduce the size of the linear system to be solved at each time step. The steps involved in the method are (1) the determination of the rank of the discrete divergence operator, A , (2) the determination of a basis for the null space of A , N ( A ), and (3) the calculation of a particular solution of the discrete continuity equation. A finite element implementation of the method is presented using quadrilateral piecewise bilinear velocity/constant pressure elements. Algorithms for the determination of a basis for N ( A ) and a particular solution are presented. Numerical comparisons of primitive versus dual variable formulations on several problems demonstrate the advantage of the dual variable method, in terms of both execution speed and memory requirements.