A 3D unsplit Forward/Backward Volume-of-Fluid approach and coupling to the level set method

This paper presents a novel methodology for interface capturing in two-phase flows by combining a Lagrangian-Eulerian Volume-of-Fluid approach with a Level Set method. While the Volume-of-Fluid transport relies on a robust and accurate polyhedral library, any high-order Level Set transport may be used. The method is shown to be less restrictive in terms of CFL conditions than split Volume-of-Fluid methods. Various geometric integration schemes are proposed and tested. For linear velocity fields, mass error is shown to vanish, and to be third order otherwise. The method is validated on 2D and 3D test cases. Conservation properties are shown to be excellent, while geometrical accuracy remains satisfactory even for complex flows such as the primary breakup of a liquid jet.