(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
We develop a new conservative Allen-Cahn phase-field model for diblock copolymers in this paper by using the Allen-Cahn type gradient flow approach for the classical Ohta-Kawaski free energy. The change in volume fraction of two composing monomers is eliminated by using a nonlocal Lagrange multiplier. Based on the recently developed stabilized Scalar Auxiliary Variable method, we have further developed an effective numerical scheme to solve the model. The scheme is highly efficient and only two linear and decoupled equations are needed to solve at every time step. We then prove that the numerical method is unconditionally energy stable, the stability and accuracy of the new scheme are demonstrated by numerous numerical examples conducted. By qualitatively comparing the equilibrium solution obtained by the new model and the classic Cahn-Hilliard model, we illustrate the effectiveness of the new model.