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A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm

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10.1002/(SICI)1097-0363(19981230)28:10<1391::AID-FLD699>3.0.CO;2-5
 
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hdl:2117/8529

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Blasco Lorente, Jorge
Codina, RamonMés informacióMés informacióMés informació
Huerta, AntonioMés informacióMés informacióMés informació
Document typeArticle
Defense date1998-12
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
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.
CitationBlasco, J.; Codina, R.; Huerta, A. A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm. "International journal for numerical methods in fluids", Desembre 1998, vol. 28, núm. 10, The definitive version is available at http://www3.interscience.wiley.com/journal/10050332/abstract, p. 1391-1419. 
URIhttp://hdl.handle.net/2117/8529
DOI10.1002/(SICI)1097-0363(19981230)28:10<1391::AID-FLD699>3.0.CO;2-5
ISSN0271-2091
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