Volume of fluid methods for immiscible-fluid and free-surface flows

This article reviews and analyzes a number of numerical methods to track interfaces in multiphase flows. Several interface tracking methods can be found in literature: the level-set method, the marker particle method, the front tracking method and the volume of fluid method (VOF) to name a few. The volume of fluid method has an advantage of being conceptually simple, reasonably accurate and phenomena such as interface breakup and coalescence are inherently included. Over the years a number of different techniques to implement the VOF method have been devised.This article gives a basic introduction to the VOF method and focuses on four VOF methods: flux-corrected transport (FCT) by Boris et al. [J.P. Boris, D.L. Book, Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works, J. Comput. Phys. 11 (1973) 38–69], Lagrangian piecewise linear interface construction (L-PLIC) by van Wachem and Schouten [B.G.M. van Wachem, J.C. Schouten, Experimental validation of 3-d Lagrangian VOF model: bubble shape and rise velocity, AIChE 48 (12) (2002) 2744–2753], Compressive interface capturing scheme for arbitrary meshes (CICSAM) by Ubbink [O. Ubbink, Numerical prediction of two fluid systems with sharp interfaces, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, 1997] and inter-gamma scheme by Jasak and Weller [H. Jasak, H.G. Weller, Interface-tracking capabilities of the InterGamma differencing scheme, Technical Report, Imperial College, University of London, 1995]. A detailed description of these schemes is given and implemented into an in-house fully coupled solver. Further, the performance of these schemes is examined employing a number of tests to analyze their strengths and weaknesses. Their advantages and limitations are discussed.