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A fractional‐step method for the incompressible Navier–Stokes equations related to a predictor–multicorrector algorithm
Author(s) -
Blasco J.,
Codina R.,
Huerta A.
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(19981230)28:10<1391::aid-fld699>3.0.co;2-5
Subject(s) - mathematics , discretization , navier–stokes equations , pressure correction method , compressibility , boundary (topology) , finite element method , dirichlet boundary condition , projection (relational algebra) , mathematical analysis , algorithm , physics , thermodynamics
An implicit fractional‐step method for the numerical solution of the time‐dependent incompressible Navier–Stokes equations in primitive variables is studied in this paper. The method, which is first‐order‐accurate in the time step, is shown to converge to an exact solution of the equations. By adequately splitting the viscous term, it allows the enforcement of full Dirichlet boundary conditions on the velocity in all substeps of the scheme, unlike standard projection methods. The consideration of this method was actually motivated by the study of a well‐known predictor–multicorrector algorithm, when this is applied to the incompressible Navier–Stokes equations. A new derivation of the algorithm in a general setting is provided, showing in what sense it can also be understood as a fractional‐step method; this justifies, in particular, why the original boundary conditions of the problem can be enforced in this algorithm. Two different finite element interpolations are considered for the space discretization, and numerical results obtained with them for standard benchmark cases are presented. © 1998 John Wiley & Sons, Ltd.