Exact Computation of the Color Function for Triangular Element 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 verify the proposed algorithm, we first compute the volume enclosed within a cubic cell for a range of synthetic configurations with known analytical solutions. We then apply the algorithm to initialize volume fraction fields on Cartesian meshes for complex interfaces and compare the results with those obtained using the existing VOFI library. The F2V results show excellent agreement with both the analytical solutions and the VOFI results, demonstrating the accuracy and robustness of the proposed approach. Finally, we evaluate the method for color function computation in multiphase flow simulations. The F2V method is compared with the conventional approach based on solving a Poisson equation, showcasing significantly improved computational efficiency, particularly on fine mesh resolutions.