Numerical simulation of the ferrohydrodynamics flow using an unconditionally stable second-order scheme

In this paper, we design a decoupled, linear, unconditionally stable and fully discrete numerical scheme for a ferrohydrodynamics system with second-order temporal accuracy. This scheme is based on a second-order backward difference formula for time derivative terms and linearization extrapolation for nonlinear terms, which produces a series of decoupled linear equations and solves effectively this nonlinear and multiphysical coupled system. Meanwhile, we show that the scheme is unconditionally stable. Finally, some numerical experiments are provided to verify the theoretical finding and illustrate the accuracy and efficiency of the proposed scheme.