Abstract
In this paper, we consider numerical approximations for solving the Cahn-Hilliard phase-field model with the Flory-Huggins-de Gennes free energy for homopolymer blends. We develop an efficient, second-order accurate, and unconditionally energy stable scheme that combines the SAV approach with the stabilization technique, in which the H1 norm is split from the total free energy and two extra linear stabilization terms are added to enhance the stability and keeping the required accuracy while using large time steps. The scheme is very easy to implement and non-iterative where one only needs to solve two decoupled fourth-order biharmonic equations with constant coefficients at each time step. We further prove the unconditional energy stability of the scheme rigorously. Through the comparisons with some other prevalent schemes like the non-stabilized-SAV and MSAV schemes for some benchmark numerical examples in 2D and 3D, we demonstrate the stability and the accuracy of the developed scheme numerically.
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Funding
J. Zhang was supported by the Science and Technology Program of Guizhou Province (No.[2020]1Y013), and Guizhou Key Laboratory of Big Data Statistics Analysis (No. BDSA20190107) .X. Yang was partially supported by NSF-DMS-1720212 and DMS-1818783.
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Communicated by: Long Chen
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Zhang, J., Yang, X. Non-iterative, unconditionally energy stable and large time-stepping method for the Cahn-Hilliard phase-field model with Flory-Huggins-de Gennes free energy. Adv Comput Math 46, 47 (2020). https://doi.org/10.1007/s10444-020-09793-z
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DOI: https://doi.org/10.1007/s10444-020-09793-z