Efficient and accurate numerical schemes for a hydrodynamically coupled phase field diblock copolymer model
This work provides efficient numerical methods for simulating complex diblock copolymer systems, which is important for materials science and polymer physics.
The authors developed second-order time marching schemes for a hydrodynamically coupled phase field diblock copolymer model, achieving linear, unconditionally energy stable, and efficiently solvable systems. Numerical experiments validated the accuracy and stability.
In this paper, we consider numerical approximations of a hydrodynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.