Exact computation of the color function for triangular element interfaces

TL;DR

This paper introduces a robust algorithm called Front2VOF for accurately computing the volume enclosed by curved surfaces discretized into triangular elements within a cube, which is crucial in computer graphics and multiphase flow simulations.

Contribution

The paper presents a novel, robust algorithm for exact volume computation of curved surface interfaces discretized into triangles within a cube.

Findings

Validated accuracy with synthetic configurations and known solutions

Demonstrated robustness across various geometric configurations

Achieved precise volume calculations for complex interfaces

Abstract

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.