发表机构
Université Claude Bernard Lyon 1, CNRS, Centrale Lyon, INSA Lyon, Université Jean Monnet, ICJ UMR5208（里昂第一大学、法国国家科学研究中心、中央里昂学院、里昂国立应用科学学院、让·莫内大学、ICJ UMR5208）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究多相穆林斯 - 谢尔克流，采用电荷模拟方法这一无网格求解器，能处理曲线网络、边界条件等，离散化结构保持，相区域守恒，经与精确解对比验证了方案在多方面的有效性。
AI 中文摘要
本文开发了一种用于二维实数空间和由诺伊曼壁界定的半平面中多相穆林斯 - 谢尔克流的整体无网格求解器。在基础数学模型中，由曲率驱动的界面通过调和化学势场耦合。采用电荷模拟方法，它是基本解方法的变体，每个化学势由曲线外电荷点处的基本解表示，无需整体网格或奇异积分。该方法处理三岔点处分离多个相的曲线网络，包括占据多个区域的相；在半平面边界上，通过镜像电荷精确施加无通量条件，移动接触保持与壁正交。离散化是结构保持的，在拓扑事件之间，通过离散面积约束的零空间投影，每个有界相区域在速度水平上以机器精度守恒。验证了该方案在收敛性、成本和条件方面与精确的三同心圆解的对比情况。
英文摘要
A charge simulation method, a variant of the method of fundamental solutions, is applied to approximate the multi-phase Mullins--Sekerka flow in $\mathbb R^{2}$ and in a half-plane bounded by a Neumann wall. In the underlying mathematical model, interfaces driven by their curvature are coupled through a harmonic chemical-potential field. Each chemical potential is represented by fundamental solutions centered at charge points off the curve, so no bulk mesh is required. The scheme treats curve networks separating several phases at triple junctions, including phases that occupy more than one region; on the half-plane boundary, the homogeneous Neumann condition is imposed exactly by image charges, and mobile contacts stay orthogonal to the wall. The discretization is structure-preserving in the sense that every bounded phase area is conserved to machine precision at the velocity level by a null-space projection of the discrete area constraints. The proposed scheme is assessed through a convergence test against an exact three-concentric-circle solution.
Comments39 pages, 13 figures, 7 tables
