Summary
We introduce and compare several smoothers for the stationary incompressible Navier-Stokes equations in primitive variables on unstructured and locally refined grids. Special emphasis is laid on the robustness of the linear multigrid solver in view of large convecting velocities and bad aspect ratios in the grid. We describe a new stream wise numbering algorithm for the unknowns with a special treatment of the cyclic dependencies due to vortices. Further we describe the implemented smoothers and show diagrams of the convergence rates (per grid level) versus the aspect ratios of the elements. Additionally we present a comparison of some theoretical results for the Stokes-solution in a corner with our calculations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bastian, P.: ug 2.0: Ein Programmbaukasten zur effizienten Lösung von Strömungsproblemen. IWR Preprint 92-14 (Univ. Heidelberg), 1992.
Bey, J., Wittum, G: To appear.
Brandt, A., Dinar, N.: Multigrid solutions to elliptic flow problems. ICASE Report 79-15 (1979).
Moffatt, K.H.: Viscous and resistive eddies near a sharp corner. Journal of Fluid Mech. 18 (1964) 1–18.
Patankar, S. V., Spalding, D.B.: A calculation procedure for heat and mass transfer in threedimensional parabolic flows. Int. J. Heat Mass Transfer 15 (1972), 1787–1806.
Schneider, G.E., Raw, M.J.: Control volume finite-element method for heat transfer and fluid-flow using colocated variables. Numer.Heat.Transf. 11 (1988) 363.
Reichert, H., Wittum, G.: Solving the Navier-Stokes-Equations on Unstructured Grids. NNFM, Vol. 39, p. 321–333, Vieweg, Braunschweig 1993.
Wittum, G.: On the Convergence of Multi-Grid Methods with Transforming Smoothers. Theory with Applications to the Navier-Stokes Equations. Numer. Math. 57 (1990) 15–38.
Wittum, G.: On the Robustness of ILU-Smoothing. SISSC 10 (1989) 699–717.
Wittum, G.: Filternde Zerlegungen: Ein Beitrag zur schnellen Lösung großer Gleichungssysteme. Habil., Univ. Heidelberg, 1990.
Wittum, G.: Distributive Iterationen für indefinite Systeme. Ph. D. Thesis, Univ. Kiel, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Reichert, H., Wittum, G. (1995). Robust Multigrid Methods for the Incompressible Navier-Stokes Equations. In: Hackbusch, W., Wittum, G. (eds) Fast Solvers for Flow Problems. Notes on Numerical Fluid Mechanics (NNFM). Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14125-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-663-14125-9_18
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07649-8
Online ISBN: 978-3-663-14125-9
eBook Packages: Springer Book Archive