标题： 三角形单元界面的颜色函数精确计算 显示英文标题

标题： Exact computation of the color function for triangular element interfaces

摘要： 由离散为三角形单元的曲面所包围的体积计算，以及立方体的计算在不同领域中具有重要意义，例如计算机图形学和多相流模拟。 我们提出了一种鲁棒的算法，即 Front2VOF（F2V）算法，以解决这个问题。 F2V 算法包含两个主要步骤。 首先，它通过分割曲面上的三角形单元来识别立方体内的多边形，仅保留位于立方体边界内的部分。 其次，它结合立方体面计算这些多边形所包围的体积。 为了验证算法的准确性和鲁棒性，我们使用了一系列具有已知解析解的合成配置对其进行测试。 显示英文摘要

摘要： The calculation of the volume enclosed by curved surfaces discretized into triangular elements, and a cube is of great importance in different domains, such as computer graphics and multiphase flow simulations. We propose a robust algorithm, the Front2VOF (F2V) algorithm, to address this problem. The F2V algorithm consists of two main steps. First, it identifies the polygons within the cube by segmenting the triangular elements on the surface, retaining only the portions inside the cube boundaries. Second, it computes the volume enclosed by these polygons in combination with the cube faces. To validate the algorithm's accuracy and robustness, we tested it using a range of synthetic configurations with known analytical solutions.