Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods

Roland GLOWINSKI; B. Mantel; J. Periaux; O. Tissier

doi:10.1007/978-3-663-14242-3_15

Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods

Roland GLOWINSKI, B. Mantel, J. Periaux, O. Tissier

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

Abstract

We use in this paper a method described in DINH-GLOWINSKIMANTEL-PERIAUX [1], for which we refer for more details for solving the time dependent Navier-Stokes equations for incompressible viscous fluids. This method combine finite elements for the space discretization and alternating directions for the time discretization. The use of the splitting associated to the alternating direction method decouples the two main difficulties of the original problem, namely non linearity and incompressibility. However this method is a natural extension of those described in [2] [3] since least squares and conjugate gradient algorithms are still the main ingredients used to treat the nonlinearity. Results of numerical experiments using this technique for the numerical simulation of the Navier-Stokes flow in a prescribed for analysis channel with a step are presented.

Original language	English
Title of host publication	Analysis of Laminar Flow over a Backward Facing Step
Subtitle of host publication	A GAMM Workshop
Editors	Ken Morgan, Jacques Periaux, François Thomasset
Publisher	Springer Vieweg+Teubner Verlag, Wiesbaden
Pages	245-267
Number of pages	23
Edition	1st
ISBN (Electronic)	9783663142423
ISBN (Print)	9783528080839
DOIs	https://doi.org/10.1007/978-3-663-14242-3_15
Publication status	Published - 1984

Publication series

Name	Notes on Numerical Fluid Mechanics
ISSN (Print)	1612-2909
ISSN (Electronic)	1860-0824

Scopus Subject Areas

General Engineering

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10.1007/978-3-663-14242-3_15

Cite this

GLOWINSKI, R., Mantel, B., Periaux, J., & Tissier, O. (1984). Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods. In K. Morgan, J. Periaux, & F. Thomasset (Eds.), Analysis of Laminar Flow over a Backward Facing Step: A GAMM Workshop (1st ed., pp. 245-267). (Notes on Numerical Fluid Mechanics). Springer Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14242-3_15

GLOWINSKI, Roland ; Mantel, B. ; Periaux, J. et al. / Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods. Analysis of Laminar Flow over a Backward Facing Step: A GAMM Workshop. editor / Ken Morgan ; Jacques Periaux ; François Thomasset. 1st. ed. Springer Vieweg+Teubner Verlag, Wiesbaden, 1984. pp. 245-267 (Notes on Numerical Fluid Mechanics).

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abstract = "We use in this paper a method described in DINH-GLOWINSKIMANTEL-PERIAUX [1], for which we refer for more details for solving the time dependent Navier-Stokes equations for incompressible viscous fluids. This method combine finite elements for the space discretization and alternating directions for the time discretization. The use of the splitting associated to the alternating direction method decouples the two main difficulties of the original problem, namely non linearity and incompressibility. However this method is a natural extension of those described in [2] [3] since least squares and conjugate gradient algorithms are still the main ingredients used to treat the nonlinearity. Results of numerical experiments using this technique for the numerical simulation of the Navier-Stokes flow in a prescribed for analysis channel with a step are presented.",

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GLOWINSKI, R, Mantel, B, Periaux, J & Tissier, O 1984, Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods. in K Morgan, J Periaux & F Thomasset (eds), Analysis of Laminar Flow over a Backward Facing Step: A GAMM Workshop. 1st edn, Notes on Numerical Fluid Mechanics, Springer Vieweg+Teubner Verlag, Wiesbaden, pp. 245-267. https://doi.org/10.1007/978-3-663-14242-3_15

Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods. / GLOWINSKI, Roland; Mantel, B.; Periaux, J. et al.
Analysis of Laminar Flow over a Backward Facing Step: A GAMM Workshop. ed. / Ken Morgan; Jacques Periaux; François Thomasset. 1st. ed. Springer Vieweg+Teubner Verlag, Wiesbaden, 1984. p. 245-267 (Notes on Numerical Fluid Mechanics).

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

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T1 - Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods

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AU - Tissier, O.

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AB - We use in this paper a method described in DINH-GLOWINSKIMANTEL-PERIAUX [1], for which we refer for more details for solving the time dependent Navier-Stokes equations for incompressible viscous fluids. This method combine finite elements for the space discretization and alternating directions for the time discretization. The use of the splitting associated to the alternating direction method decouples the two main difficulties of the original problem, namely non linearity and incompressibility. However this method is a natural extension of those described in [2] [3] since least squares and conjugate gradient algorithms are still the main ingredients used to treat the nonlinearity. Results of numerical experiments using this technique for the numerical simulation of the Navier-Stokes flow in a prescribed for analysis channel with a step are presented.

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GLOWINSKI R, Mantel B, Periaux J, Tissier O. Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods. In Morgan K, Periaux J, Thomasset F, editors, Analysis of Laminar Flow over a Backward Facing Step: A GAMM Workshop. 1st ed. Springer Vieweg+Teubner Verlag, Wiesbaden. 1984. p. 245-267. (Notes on Numerical Fluid Mechanics). doi: 10.1007/978-3-663-14242-3_15

Finite Element Analysis of Laminar Viscous Flow Over a Step by Nonlinear Least Squares and Alternating Direction Methods

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