Non-convex analytical and geometrical tools for volume truncation, initialization and conservation enforcement in VOF methods

© 2019 The Author(s) A set of non-convex calculation tools for volume of fluid (VOF)methods in general grids is presented. The complexity of the volume truncation operation and the computation of the interface position to cut off a certain liquid volume fraction from a cell, involved in VOF methods, is greatly increased when non-convex grids and polytopes are considered. Therefore, the tools for convex geometries developed in a previous work by López and Hernández (2008)[32]have required profound adaptation for the different algorithms not only to address the challenges of the new geometry, but also to maintain the efficiency and robustness of previous tools. Also, a new method for the liquid volume initialization in general polygonal and polyhedral cells, either convex or non-convex, is proposed. A comparison with conventional procedures based on convex decomposition is carried out using different tests, whereby it is demonstrated that the proposed tools represent a substantial improvement in computational efficiency. Overall, a speedup of around one order of magnitude is achieved for the reconstruction of several 2D and 3D interfacial shapes.