2025/06/08 by Dawei Chen, Chen, Dawei, Minghui Li +2
Engineering · Materials Science · Mathematics · #65M12 #65M70 #74A50 #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods for differential equations #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2506.07128
openalex publication_date 2025/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.