Abstract
The problem of singularities caused by boundary conditions is studied on the flow in lid driven cavity. The asymptotic behaviour of pressure near the singularity locations is used together with the a priori error estimates of the finite element solution, in order to design the finite element mesh adjusted to singularity. In this way a very precise solution in the vicinity of the singularity is obtained. A posteriori error estimates are used as the principal tool for error analysis. Numerical results showing the dramatic improvement in pressure calculation are presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1967)
Burda, P.: On the FEM for the Navier-Stokes equations in domains with corner singularities. In: Křížek, M., et al. (eds.) Finite element methods, Supeconvergence, post-processing and a posteriori estimates, pp. 41–52. Marcel Dekker, New York, NY (1998)
Burda, P., Novotný, J., Sousedík, B.: A posteriori error estimates applied to flow in a channel with corners. Math. Comput. Simul. 61, 375–383 (2003)
Burda, P., Novotný, J., Šístek, J.: Precise FEM solution of a corner singularity using an adjusted mesh. Int. J. Numer. Meth. Fluids 47, 1285–1292 (2005)
Burda, P., Novotný, J., Šístek, J.: Accurate solution of corner singularities in axisymmetric and plane flows using adjusted mesh of finite elements. In: Groth, C., Zingg, D. W. (eds.) Computational Fluid Dynamics 2004, Proceedings of the Third International Conference on Computational Fluid Dynamics, ICCFD, pp. 463–468. Springer, Berlin (2006)
Girault, V., Raviart, P.G.: Finite Element Method for Navier-Stokes Equations. Springer, Berlin (1986)
Kondratiev, V.A.: Asimptotika rešenija uravnienija Nav’je-Stoksa v okrestnosti uglovoj točki granicy. Prikl. Mat. i Mech. 1, 119–123 (1967)
Ladevéze, J., Peyret, R.: Calcul numérique d’une solution avec singularité des équations de Navier-Stokes: écoulement dans un canal avec variation brusque de section. Journal de Mécanique 13, 367–396 (1974)
Luchini, P.: Higher-order difference approximations of the Navier-Stokes equations. Int. J. Numer. Meth. Fluids 12, 491–506 (1991)
Acknowledgments
This work has been supported by the grant No. 106/08/0403 - GACR, by the State Research Project No. MSM 684 0770010, and by Institutional Research Plan AV0Z10190503.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burda, P., Novotný, J., Šístek, J. (2011). Singularities in Lid Driven Cavity Solved by Adjusted Finite Element Method. In: Kuzmin, A. (eds) Computational Fluid Dynamics 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17884-9_101
Download citation
DOI: https://doi.org/10.1007/978-3-642-17884-9_101
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17883-2
Online ISBN: 978-3-642-17884-9
eBook Packages: EngineeringEngineering (R0)