Three-dimensional cellwise conservative unsplit geometric VOF schemes

This work presents two unsplit geometric VOF schemes that extend the two-dimensional cellwise conservative (CCU) scheme (Comminal et al. (2015) [49]) to three dimensions. The novelty of 3D-CCU lies in representation streaksurfaces donating regions by polyhedral surfaces whose vertices are calculated with 4th order Runge-Kutta scheme. Moreover, advected liquid volumes computed using a truncation algorithm (López (2019) [62]) suited for arbitrary non-convex and self-intersecting polyhedra, which removes need tetrahedral decomposition. advection were coupled interface reconstruction methods (Youngs' method, Mixed Youngs-Centered scheme, Least-Square Fit algorithm). resulting tested classical benchmark tests, including translation, rigid-body rotation, shear deformation flows. proposed conserve volume maintain physical boundedness fractions machine precision. perform favorably compared other when Youngs' method. more accurate than most use second-order reconstruction, except those where 3D extension Mosso-Swartz is employed. comparison different highlights importance coupling schemes.