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arXiv · 2506.07128

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

Dawei Chen·Qinzhen Ren·Minghui Li
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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-step 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-step algorithms is given, and the advantages of the new adaptive time-step algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments.

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BibTeXRIS

Dawei Chen, Qinzhen Ren, Minghui Li. 2025-06-08. New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system. https://arxiv.org/abs/2506.07128

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