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

Abstract 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 Lopez and Hernandez (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.

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