  Available algorithms for the initialization of volume fractions typically
utilize exact functions to model fluid interfaces, or they rely on
computationally costly intersections between volume meshes. Here, a new
algorithm is proposed that computes signed distances and volume fractions on
unstructured meshes from arbitrarily shaped surfaces, e.g. originating from
experimental data. The proposed algorithm calculates signed distances
geometrically near the fluid interface, approximated as a triangle surface
mesh, and propagates the inside/outside information by an approximate solution
of a Laplace equation. Volume fractions are computed based on signed distances,
using either geometrical intersections between cells of the unstructured mesh
and a sub-set of the surface mesh that represents the interface, or using a
polynomial approximation and adaptive mesh refinement. Although primarily
developed for multiphase flow simulations, the proposed algorithm can
potentially be used for other problems that require a phase-indicator:
inside/outside information with respect to an arbitrarily shaped surface on
arbitrarily unstructured meshes.
