The paper focuses on modelling free surface flow. The interface is modelled using the Volume-Of-Fluid method, where the advection of volume fractions is treated by a purely geometrical method. The novelty of the work lies in the way that it incorporates Binary Space-Partitioning trees for computing the intersections of polyhedra. Volume-conserving properties and shape-preserving properties are presented on two benchmarks and on a simulation of the famous broken dam problem.