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New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system.

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Title: New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system.
Authors: Chen, Dawei1 (AUTHOR) cdwstnu@163.com, Ren, Qinzhen1 (AUTHOR) qzhen2017@163.com, Li, Minghui1 (AUTHOR) minghuili_xmu@163.com
Source: Computers & Mathematics with Applications. Feb2026, Vol. 204, p182-197. 16p.
Subjects: Relaxation methods (Mathematics), Numerical analysis, Cahn-Hilliard-Cook equation, Simulation methods & models, Iterative methods (Mathematics), Stability of linear systems
Abstract: In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-stepping algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-stepping algorithms is given, and the advantages of the new adaptive time-stepping algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-stepping algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-stepping algorithms is given, and the advantages of the new adaptive time-stepping algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2025.12.016