Efficient numerical scheme for a new hydrodynamically-coupled conserved Allen-Cahn type Ohta-Kawaski phase-field model for diblock copolymer melt

In this work, we first propose a new hydrodynamically-coupled phase-field model for the diblock copolymer melt that is derived based on the Allen-Cahn dynamics where the volume fraction of two composing monomers is conserved by using a nonlocal Lagrange multiplier. Formally, the system is a highly nonlinear system that consists of the incompressible Navier-Stokes equations and a nonlocal-type Allen-Cahn type equation. Then, to solve the model, we develop a linear and second-order time-marching scheme via the Invariant Energy Quadratization approach with the stabilization technique for the nonlinear potentials, as well as the projection method for the Navier-Stokes equations. The unconditional energy stability of the numerical method is proved, and several experiments of 2D and 3D are performed to validate the accuracy and energy stability of the developed numerical scheme. (C) 2020 Elsevier B.V. All rights reserved.