Numerical Simulation of Magnetic Droplet Dynamics in a Rotating Field

Abstract

Dynamics and hysteresis of an elongated droplet under the action of a rotating magnetic field is considered for mathematical modelling. The shape of droplet is found by regularization of the ill-posed initial–boundary value problem for nonlinear partial differential equation (PDE). It is shown that two methods of the regularization – introduction of small viscous bending torques and construction of monotonous continuous functions are equivalent. Their connection with the regularization of the ill-posed reverse problems for the parabolic equation of heat conduction is remarked.

Spatial discretization is carried out by the finite difference scheme (FDS). Time evolution of numerical solutions is obtained using method of lines for solving a large system of ordinary differential equations (ODE).

Keywords:

• magnetic field
• hysteresis
• ill posed problem
• finite differences

AMS Subject Classification:

• 65M06
• 65M20
• 65M70
• 65N06
• 65F22
• 65N20
• 65N40