Abstract
The present study is devoted to the development of an ADI approach to simulate two-dimensional time-dependent diffusion process of ferromagnetic particles in magnetic fluids. Specific features of the problem are the Neumann boundary conditions. We construct an ADI scheme of formally second order accuracy approximation in time and space. It is proved that the scheme is absolutely stable and it has the accuracy in the energy norm of the second order in time and the order 3/2 in space. The numerical results of a test problem indicate that the convergence rate in space is of the second order as well.
Highlights
Papers related to a study of the diffusion process of ferromagnetic particles take a considerable place in the hydromechanics of magnetic fluids
In [1, 2] twodimensional time-dependent problems on steadying the particle concentration distribution with time in a rectangular magnetic-fluid domain are solved by means of a finite-difference scheme of alternating direction (ADI) type
The present study is devoted to the development of an ADI approach to time-dependent particle diffusion problems, specific features of which are the boundary conditions of the Neumann type
Summary
Papers related to a study of the diffusion process of ferromagnetic particles take a considerable place in the hydromechanics of magnetic fluids. Using this solution, two ferrohydrostatic problems on the influence of the particle diffusion have been solved numerically: on axisymmetric equilibrium shapes of a free magnetic-fluid surface in the magnetic field of a cylindrical conductor with direct current [3] and on the instability of a horizontal magnetic-fluid layer in a uniform magnetic field [7]. In [1, 2] twodimensional time-dependent problems on steadying the particle concentration distribution with time in a rectangular magnetic-fluid domain are solved by means of a finite-difference scheme of alternating direction (ADI) type. The present study is devoted to the development of an ADI approach to time-dependent particle diffusion problems, specific features of which are the boundary conditions of the Neumann type. Notice that in the case of Dirichlet boundary conditions, the ADI scheme for the modified concentration equation is studied in [12]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
