Finite Element Methods for Coupled Problems in Ferrohydrodynamics

Linear and nonlinear approach to the Rosensweig instability

“…For bounding the computational domain in the x − y plane we consider only one cell of an developed pattern and use the corresponding wavelength as a characteristic length scale for the dimensionless computation. This approach has been successfully applied in [17,18]. However, in this way it is impossible to find the preferred pattern, like hexagons, squares, or the newly observed solitons (see section 3.2 and Ref.…”

“…For this a parametrization of the free surface is needed. The 2d axisymmetric case in a parametric setting has been studied in [17], for the full 3d case and surfaces of graph type see [18]. From an algorithmic point of view, the big challenge in this approach is the coupling of 3d field calculations with the 2d free surface equation (12) on one cell of the developed pattern.…”

Numerical Study of Diffusion of Interacting Particles in a Magnetic Fluid Layer

“…It allows us to study axisymmetric solutions of the presented model in a two-dimensional geometry of cylindrical coordinates. Axisymmetric solutions on a circular cell were compared with three-dimensional ones on a hexagonal cell in (Lavrova et al, 2003). It was found that the profile shapes of both models nearly completely coincides.…”

“…The numerical results concern equilibrium states of the ferrofluid layer in (Aristidopoulou et al, 1996;Bashtovoi et al, 2002;Boudouvis et al, 1987;Gollwitzer et al, 2007;2009;Lavrova et al, 2003;2010) and analyze dynamical properties of the ferrofluid 9 www.intechopen.com behavior in (Knieling et al, 2007;Matthies & Tobiska, 2005). A non-uniform equilibrium distribution of particles in the ferrofluid layer is computed in (Lavrova et al, 2010) for the first time.…”

Modeling of Membrane Reactors

“…The package is in particular suited for the solution of incompressible fl ow problems in two -and threedimensional domains decomposed into triangular/tetrahedral and quadrilateral/ hexahedral meshes, respectively. Several benchmark computations have been performed using MooNMD which show its high accuracy and wide range of applicability (John, 2002 ;Lavrova et al ., 2002 ;Iliescu et al , 2003 ). The most important features of MooNMD are:…”