Title: Efficient and accurate numerical schemes for a hydrodynamically coupled phase field diblock copolymer model,
Abstract: 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.