用于间歇性和孤立拓扑转变的尖锐-扩散界面模型
A sharp-diffuse interface model for intermittent and isolated topological transitions
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中文总结 AI 辅助
针对Cahn-Hilliard相粗化的拓扑转变问题，提出混合尖锐-扩散界面模型，结合边界积分与界面手术算法，模拟界面合并的质量交换问题，实现比传统方法高两到三个数量级的加速。
中文摘要 AI 辅助
我们提出一种混合尖锐-扩散界面表示方法，用于建模Cahn-Hilliard相粗化过程中的间歇性和孤立拓扑转变。在远离拓扑事件时，演化由Mullins-Sekerka尖锐界面极限系统近似，并采用边界积分格式计算；当扩散过渡层重叠时，一种新型界面手术算法通过局域化Cahn-Hilliard伪时间演化解析拓扑变化，之后恢复尖锐界面计算。我们开发了该分解背后的数学公式，给出了简单的二维数值实现，并模拟了界面合并的质量交换问题。通过将扩散演化局域化到拓扑事件，该方法比传统扩散界面模拟实现了两到三个数量级的加速。
英文摘要
We propose a hybrid sharp-diffuse interface representation for modeling intermittent and isolated topological transitions during Cahn-Hilliard phase coarsening. Away from topological events, the evolution is approximated by the Mullins-Sekerka sharp-interface limit system and computed using a boundary integral formulation. When diffuse transition layers overlap, a novel interface surgery algorithm resolves topology changes through a localized Cahn-Hilliard pseudo-time evolution, after which the sharp-interface calculation is resumed. We develop the mathematical formulation underlying this decomposition, present a simple two-dimensional numerical implementation, and simulate a mass-exchange problem with interface coalescence. By localizing the diffuse evolution to topological events, the method achieves a speedup of two to three orders of magnitude over conventional diffuse-interface simulations.
