New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system
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| Format: | Preprint |
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2025
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| _version_ | 1866918050296496128 |
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| author | Chen, Dawei Ren, Qinzhen Li, Minghui |
| author_facet | Chen, Dawei Ren, Qinzhen Li, Minghui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system Chen, Dawei Ren, Qinzhen Li, Minghui Numerical Analysis Computational Physics 74A50, 65M12, 65M70 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. |
| title | New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system |
| topic | Numerical Analysis Computational Physics 74A50, 65M12, 65M70 |
| url | https://arxiv.org/abs/2506.07128 |