Numerical simulation of normal-field instability in the static and dynamic case

Abstract The normal-field instability is studied numerically by a finite element approach based on the 3D equations for the magnetostatic potential and the 3D Navier–Stokes equations for the velocity and pressure fields of the magnetic fluid. The finite element method is able to determine the critical value of the magnetic field intensity for the onset of the instability and to describe the transition from the undisturbed surface to the fully developed pattern in the dynamic case.