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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References
Q.V. DINH, B. MANTEL, J. PERIAUX, R. GLOWINSKI, On the numerical simulation of incompressible viscous fluids modelled by the Navier-Stokes equations, related domain decomposition methods. Refined modelling of flows Paris, September 7th-10th, 1982.
BRISTEAU M.O., GLOWINSKI R., PERIAUX J., PERRIER P., PIRONNEAU O., POIRIER G., Application of Optimal Control and Finite Element Methods to the Calculation of Transonic Flows and Incompressible Viscous Flows, in Numerical Methods in Applied Fluid Dynamics B. Hunt Ed., Academic Press, London, 1980, 203–312.
BRISTEAU M.O., GLOWINSKI R., MANTEL B., PERIAUX J., PERRIER,P., PIRONNEAU O., A Finite Element Approximation of Navier-Stokes Equations for Incompressible Viscous Fluids. Iterative methods of solution, in Approximation Methods for Navier-Stokes problems,R Rautmann Ed., Lecture Notes in Mathematics, Vol. 771, Springer-Verlag, Berlin, 1980, 78–128.
GLOWINSKI R., PIRONNEAU O., On numerical methods for the Stokes problem, in: Energy methods in Finite Element Analysis, R. Glowinski, E.Y. Rodin, O.C. Zienkiewicz (Eds.), J. Wiley and Sons, Chichester, 1979, Chap. 13, pp. 243–264.
TAYLOR C., HOOD P., A Numerical solution of the NavierStokes Equations using the Finite Element Technique, Computer and Fluids, 1, pp. 73–100, (1973).
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© 1984 Springer Fachmedien Wiesbaden
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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: Morgan, K., Periaux, J., Thomasset, F. (eds) Analysis of Laminar Flow over a Backward Facing Step. Notes on Numerical Fluid Mechanics, vol 9. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14242-3_15
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DOI: https://doi.org/10.1007/978-3-663-14242-3_15
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08083-9
Online ISBN: 978-3-663-14242-3
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