An unconditionally stable variable time step scheme for two-phase ferrofluid flows

Abstract

In this paper, a decoupled, linearized, unconditionally stable, and fully discrete numerical scheme is presented for simulating two-phase ferrofluid flows. This scheme is constructed by introducing two scalar auxiliary variables. It is based on the backward Euler scheme with variable time step and mixed finite element discretization. Nonlinear terms are treated explicitly to simplify the computational process. Meanwhile, without any restriction on time step, we show the stability of the proposed scheme. Finally, numerical examples are presented to check the accuracy and efficiency of the proposed scheme.