Abstract
This paper describes a numerical method for solving the time dependant Navier Stokes equations for incompressible viscous fluid flows. The method results from a three step implicit scheme for the time discretization and from a finite element approximation for the space discretization. The typical fractional step method leads to an uncoupling between the non linearity and incompressibility and the convective terms appear in a linearized semi-implicit form. The discretization avoids the use of Least Squares methods to treat the non linearity, it has shown excellent convergence properties which improve as the Reynolds number increases. Conjugate gradients algorithms are especially developed for solving the resulting linear systems including unsymmetrical matrices. For convection dominated flows, a balancing dissipation technique is introduced in order to stabilize the oscillatory nature of the solution.
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References
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© 1984 Springer Fachmedien Wiesbaden
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Buffat, M., Brison, J.F., Carriere, P., Serres, E., Jeandel, D. (1984). An Efficient Quasi-Linear Finite Element Method for Solving the Incompressible Navier-Stokes Equations at Large Reynolds Numbers. 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_8
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DOI: https://doi.org/10.1007/978-3-663-14242-3_8
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08083-9
Online ISBN: 978-3-663-14242-3
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