The initialisation of volume fractions for unstructured grids using implicit surface definitions

The use of the Volume of Fluids method [1] for interface flow calculations requires the initialisation of a free surface, typically a liquid-gas interface. Such initialisations require the translation of implicit functions, describing the topology of the interface, onto a computational grid. In grid cells where both fluids are present, some volume fraction or percentage fill must be calculated. For a number of industrial problems, a Cartesian mesh may not be optimal and an unstructured grid is desired. In this paper, a new tool is developed for initialising the volume fraction on an arbitrary unstructured grid. The approach comprises three steps, the first is to decompose a computational cell into simplexes. Next, each simplex is intersected with the free surface forming a new sub polytope whose volume can be computed analytically. The final step involves computing the volume between the polytope faces and the free surface using numerical quadrature. The proposed method is demonstrated on unstructured grids and shown to be both robust and accurate. (C) 2018 Elsevier Ltd. All rights reserved.