Comparison of semi‐analytical and FEM solutions in a certain magnetic fluid dynamics problem

Abstract

Purpose

To provide a new semi‐analytical procedure which is much faster than FEM and for this reason can be applied in a reconstruction of an interface between two conducting fluids (magnetic fluid dynamics problem) by means of magnetic field tomography.

Design/methodology/approach

Three approaches are compared: a simple analytical solution (AS1), a modified semi‐analytical solution (AS2), and the finite element method solution. The modified semi‐analytical approach takes into account an information about azimuthal spatial harmonics received from the Fourier analysis of magnetic flux density distributions calculated by FEM. AS1 and AS2 have been compared for different modes of the interface using FEM solution as a reference.

Findings

It is shown that for small perturbations the AS2 in every case provides smaller errors than AS1 although for some modes (14,24) the quality of the solution is still not satisfactory.

Originality/value

This paper describes a new technique for the analysis of electromagnetic field which can be also applied in other problems.

Citation

Ziolkowski, M., Brauer, H. and Kuilekov, M. (2005), "Comparison of semi‐analytical and FEM solutions in a certain magnetic fluid dynamics problem", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 2, pp. 418-426. https://doi.org/10.1108/03321640510586051