A SPH solver for simulating paramagnetic solid fluid interaction in the presence of an external magnetic field

The Smoothed Particle Hydrodynamics (SPH) method is extended to solve magnetostatic problems involving magnetically interacting solid bodies. In order to deal with the jump in the magnetic permeability at a fluid-solid interface, a consistent SPH scheme is utilized and a modified formulation is proposed to calculate the magnetic force density along the interface. The results of the magnetostatic solver are verified against those of the finite element method. The governing fluid flow equations are discretized using the same SPH scheme, developing an efficient method for simulating the motion of paramagnetic solid bodies in a fluid flow. The proposed algorithm is applied to a benchmark problem including a suspended paramagnetic solid body moving under the influence of a non-uniform magnetic field and the result is validated against literature. The proposed method is further verified by simulating the magneto-hydrodynamic interaction of two suspended circular cylinders. As a more complex test-case, the evolution of a suspended magnetic chain under the influence of a rotating magnetic field is also simulated. The deformation of a chain formed by a number of paramagnetic solid bodies in a shear flow is simulated. Steady state and dynamic responses of the magnetic chain are investigated under steady and oscillatory shear flows. The effects of Reynolds number, solid volume fraction, strength of the external magnetic field and the number of solid bodies forming the chain, are discussed.