A new class of algorithms that preserve mass exactly for incompressible flows on a Cartesian mesh are presented. They amount to piecewise-linear, area-preserving mappings of tessellations of the plane. They are equivalent to Volume-of-Fluid (VOF) advection methods which are decomposed into an Eulerian implicit scheme in one direction followed by a Lagrangian explicit step in the other one. It is demonstrated that mass conservation is exact for incompressible flows and that there are no undershoots or overshoots of the volume fraction which thus always remains constrained between 0 and 1. © 2003 Elsevier B.V. All rights reserved.
Aulisa, E., Manservisi, S., Scardovelli, R., & Zaleski, S. (2003). A geometrical area-preserving Volume-of-Fluid advection method. Journal of Computational Physics, 192(1), 355–364. https://doi.org/10.1016/j.jcp.2003.07.003