Abstract
The interaction between a magnetisable fluid and an external magnetic field gives rise to several interesting phenomena in ferrohydrodynamics. Our mathematical models and solution strategies are mainly focused on cases in which the magnetic liquid exhibits a free surface which is not known a-priori. In particular, two special problems are taken into consideration: the behaviour of a ferrofluid drop in a rotary shaft seal and the generation of an ordered pattern of surface protuberances when the applied field exceeds a critical value.
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
Preview
Unable to display preview. Download preview PDF.
References
Auernhammer, G. K., Brand, H. R.: Thermal convection in a rotating layer of a magnetic fluid. Eur. Phys. J. B 16 (2000) 157–168
Bänsch, E., Höhn, B.: Numerical treatment of the Navier-Stokes equations with slip boundary condition. SIAM J. Sci. Comp. 20 (2000) 2144–2162
Berkovsky, B. M., Bashtovoy, V.: Magnetic Fluids and Applications Handbook. Begell house, Inc., New York, Wallingford (UK), 1996
Cowley, M. D., Rosensweig, R. E.: The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 30 (1967) 671–688
Friedrichs, R., Engel, A.: Pattern and wavenumber selection in magnetic fluids. Phys. Rev. E 64 (2001) 021406
Gailitis, A.: Formation of hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field. J. Fluid Mech. 82 (1977) 401–413
Girault, V., Raviart, P.: Finite element methods for Navier-Stokes equations. Theory and algorithms Springer-Verlag, Berlin, 1986
John, V., Knobloch, P., Matthies, G., Tobiska, L.: Non-nested multi-level solvers for finite element discretizations of mixed problems. Computing 68 (2002) 343–373
John, V., Matthies, G.: MooNMD - a program package based on mapped finite element methods. Technical Report 02–01, Fakultät für Mathematik, Otto-vonGuericke-Universität Magdeburg (2002)
Matthies, G.: Finite element methods for free boundary value problems with capillary surface. Shaker Verlag, Aachen, 2002, PhD thesis, Otto-von-GuerickeUniversität Magdeburg
Matthies, G., Tobiska, L.: Simulation of free surfaces of magnetic liquids. In: Algoritmy 2000, 15th Conf. Scientific Comput., ed. by Handlovicová, A., et. all, Slovak Technical University, Bratislava (2000) 1–10
Mitkova, T.: Lösbarkeit eines mathematischen Modells für Dichtungen mit magnetischen Flüssigkeiten. Technische Mechanik 20 (2000) 283–293
Odenbach, S.: Magnetoviscous effects in ferrofluids. Lect. Notes Physics, m71, 2002
Polevikov, V.: Stability of a static magnetic-fluid seal under the action of an external pressure drop. Fluid Dynamics 32 (1997) 457–461
Polevikov, V.: Numerical modelling of equilibrium capillary surfaces: some methods and results. Preprint 98–10, Fakultät für Mathematik, Otto-von-GuerickeUniversität Magdeburg (1998)
Polevikov, V.: Methods of numerical modeling of equilibrium capillary surfaces. Differents. Uravnenia 35 (1999) 975–981
Polevikov, V., Tobiska, L.: Modeling of a dynamic magneto-fluid seal in the presence of a pressure drop. Fluid Dynamics 36 (2001) 890–898
Rosensweig, R. E.: Ferrohydrodynamics. Dover Publications, Inc. Mineola, New York, 1997
Saad, Y.: Iterative method for sparse linear systems. PWS Publishing Company, 1996
Vanka, S.: Block-implicit multigrid calculation of two-dimensional recirculating flows. Comp. Meth. Appl. Mech. Eng. 59 (1986) 29–48
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lavrova, O., Matthies, G., Mitkova, T., Polevikov, V., Tobiska, L. (2003). Finite Element Methods for Coupled Problems in Ferrohydrodynamics. In: Bänsch, E. (eds) Challenges in Scientific Computing - CISC 2002. Lecture Notes in Computational Science and Engineering, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19014-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-19014-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62406-3
Online ISBN: 978-3-642-19014-8
eBook Packages: Springer Book Archive