Stokes-Cahn-Hilliard方程的二阶并行解耦算法
Second-Order Parallel Decoupled Algorithms for the Stokes-Cahn-Hilliard Equation
摘要: 本文为Stokes-Cahn-Hilliard相场模型开发了一种具有二阶时间精度的时间并行解耦算法，在时间上基于谱延迟校正方法和时间并行Parareal算法。此外，我们使用稳定化方法处理Cahn-Hilliard方程，运用了压力投影方法处理Stokes方程中压力p和速度u的耦合。相较于解耦的方案，进一步提高了算法的计算效率。最后，通过数值实验证明了它的稳定性和高效性。
Abstract: In this paper, we develop a time-parallel decoupled algorithm with second-order temporal accuracy for the Stokes-Cahn-Hilliard phase-field model, based in time on the spectral-deferred correction method and the time-parallel Parareal algorithm. In addition, we use a stabilisation method for the Cahn-Hilliard equation and employ a pressure projection method for the coupling of pressure p and velocity u in the Stokes equation. Compared with the decoupled scheme, the computational efficiency of the algorithm is further improved. Finally, numerical experiments demonstrate its stability and efficiency.
文章引用：刘鑫. Stokes-Cahn-Hilliard方程的二阶并行解耦算法[J]. 应用数学进展, 2025, 14(4): 765-774. https://doi.org/10.12677/aam.2025.144204

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