Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials

Abstract

We consider in this paper numerical approximations of the immiscible binary mixture of nematic liquid crystals (LCs) and viscous fluids. We develop a second-order time marching scheme by adopting the recently developed stabilized-SAV (scalar auxiliary variable) approach where several critical stabilization terms are added to enhance the stability; thus, large time steps are allowed in computations. The scheme is highly efficient and one only needs to solve several decoupled linear equations with constant coefficients at each time step. The energy stability of the scheme is proved, and various 2D and 3D numerical experiments including the drop deformations and phase separations are then performed to validate the accuracy and energy stability of the proposed scheme.