Analytical and geometrical tools for 3D volume of fluid methods in general grids

It is well known that volume of fluid (VOF) methods in three-dimensions, especially those based on unsplit advection schemes, involve highly complex geometrical operations. The objective of this work is to propose, for general grids and three-dimensional Cartesian geometry, simple and efficient geometrical tools for volume truncation operations that typically arise in VOF methods and an analytical method for local volume enforcement. The results obtained for different tests and grid types show that the proposed analytical method may be as much as three times faster than Brent’s iterative method. Advection tests were carried out using hexahedral grids obtained from deformation of a cubic grid to assess the accuracy of the proposed tools in combination with a recently proposed unsplit PLIC–VOF method.