Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 260, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cpc.2020.107290
Keywords
Copolymer; homopolymer mixtures; Coupled Cahn-Hilliard system; Decoupling; Unconditional energy stability; SAV approach
Funding
- Science Challenge Project [TZ2016002]
- China Scholarship Council (CSC) [201806280137]
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In this paper, numerical approximations for a coupled Cahn-Hilliard system are discussed, aiming at describing phase separation of copolymer and homopolymer mixtures. Two efficient, decoupled, and linear numerical schemes are proposed using the Scalar Auxiliary Variable (SAV) approach, leading to decoupled linear equations with constant coefficients at each time step. Numerical examples and benchmark simulations are conducted to demonstrate the accuracy and energy stability of the proposed schemes.
The numerical approximations for the coupled Cahn-Hilliard system describing the phase separation of the copolymer and homopolymer mixtures are considered in this paper. To develop easy to implement time marching schemes with unconditional energy stabilities, we use the Scalar Auxiliary Variable (SAV) approach for achieving two efficient, decoupled, and linear numerical schemes, where a new scalar auxiliary variable is introduced to reformulate the model. The schemes lead to decoupled linear equations with constant coefficients at each time step, and their unique solvability and unconditional energy stabilities are proved rigorously. Numerical examples are performed to demonstrate the accuracy and energy stability of the proposed schemes, and numerous benchmark simulations are also presented to show a variety of morphologies of pattern formations of the copolymer and homopolymer mixtures. (C) 2020 Elsevier B.V. All rights reserved.
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