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Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen–Cahn-type block copolymer (BCP) model

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Abstract

In this paper, the numerical approximations of a new, Allen–Cahn-type block copolymer (BCP) model describing the phase transition of the block copolymer and homopolymer mixtures are considered. We first derive a new Allen–Cahn-type coupled phase-field model by using the L2-gradient flow and add two nonlocal Lagrange multipliers to the system to conserve the mass for each component. Then, we develop a series of efficient, unconditionally energy stable, non-iterative schemes based on the SAV, 3S-SAV, and new Lagrange multiplier approaches. At each time level, the developed numerical schemes are reduced to decoupled linear equations with constant coefficients, and their unconditional energy stabilities are strictly proved. Numerical examples are provided to validate the accuracy and energy stability of the schemes, and ample simulations are conducted to show the various pattern morphologies.

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Funding

Qi Li’s work is supported by the Fundamental Research Funds for the Central Universities, CHD (No. 300102121302), and the National Natural Science Foundation of China (No. 12101073). Supei Zheng’s work is supported by the National Natural Science Foundation of China (No. 11971075).

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, Shaanxi, 710064, People’s Republic of China

    Qi Li & Supei Zheng

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China

    Liquan Mei

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  1. Qi Li
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Correspondence to Supei Zheng.

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Li, Q., Zheng, S. & Mei, L. Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen–Cahn-type block copolymer (BCP) model. Numer Algor 92, 1233–1259 (2023). https://doi.org/10.1007/s11075-022-01338-3

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