Magneto-fluid-structure interaction issues for vibrating rigid bodies in conducting fluids: The numerical and the analytical approaches

To study the magneto-fluid-structure interaction (MFSI) problems for rigid bodies and conducting fluids, a numerical method and an analytical approach have been carried out. The numerical scheme is based on a partitioned arbitrary Lagrangian-Eulerian framework, and is suitable for viscous, incompressible magneto-fluid-structure interaction simulation. A displacement prediction-pressure stabilization scheme has been established to enhance the stability and efficiency. Meanwhile, a consistent and conservative scheme for deforming configurations has been developed. This method can numerically ensure the divergence-free condition of the current density, and can conserve the momentum from the Lorentz forces after grids update. The analytical approach has considered a vibrating cylinder surrounded by confined fluids in a magnetic field. By assuming a small amplitude and a low magnetic Reynolds number, the analytical solution can describe the temporal and spatial distribution of the fluid fields, the electromagnetic fields, and the solid motion. These solutions are also suitable for general fluid-structure interaction (FSI) problems. Comparative results suggest good agreement between the two methods developed in this paper. Nonlinear effects of the magnetic fields were presented and discussed based on the numerical results. These cases are based on careful validations, and can hopefully be used for future verification and validation work.