This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.

翻译：本文介绍了一种在非结构化三角形网格上保持体积守恒的界面追踪算法。我们提出通过三角形边切割来离散化界面，该方法使用每个三角形6个数值的紧凑表示来记录界面与三角形网格边的交点。这使得我们能够高效地隐式表示子三角形多边形材料区域，而无需显式存储连接信息。此外，我们针对该界面表示提出了一种高效的对流算法，该算法基于几何查询且无需优化过程。此对流算法通过面积校正步骤进行扩展，以强制保持材料的体积守恒。我们在三角形网格上的多种对流问题中验证了本方法的有效性，并将其性能与包括VOF和MOF在内的现有界面追踪方法进行了比较。