Three-dimensional cellwise conservative unsplit geometric VOF schemes

• Published in: Journal of computational physics Vol. 442; p. 110479
• Main Authors: Comminal, Raphaël, Spangenberg, Jon
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.10.2021; Elsevier Science Ltd
• Subjects: Advection; Algorithms; Apexes; Cellwise advection; Computational physics; Least squares; Reconstruction; Rotating bodies; Runge-Kutta method; Semi-Lagrangian tracking; Three dimensional flow; Unsplit geometric scheme; Volume conservation; Volume-of-fluid method; Volume-of-fluid method; Semi-Lagrangian tracking; Unsplit geometric scheme; Cellwise advection; Volume conservation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110479

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