A fully-decoupled energy stable scheme for the phase-field model of non-Newtonian two-phase flows

In this paper, we first propose a novel fully-decoupled, linear and second-order time accurate scheme to solve the phase-field model of non-Newtonian two-phase flows; the developed scheme is based on a stabilized Scalar Auxiliary Variable (SAV) approach. We strictly prove the unconditional energy stability of the scheme and conduct a numerical simulation to show the accuracy and stability of the proposed scheme. Moreover, we can observe that the parameter $r$ in non-Newtonian fluids can affect spatial patterns during phase transitions, which directly enables us to design and perform optimal control experiments in engineering processes.