Exact computation of the color function from piecewise linear interfaces

A good evaluation of the color function is of importance in the simulation of multiphase flows, both for use in obtaining accurate surface tension and generally for capturing realisitc physics. The errors of some methods such as the Front-Tracking method are especially acute when the density ratio is large. Then small errors in the color evaluation can lead to large errors in the density, and as a consequence erroneous velocity field. A new geometric computation of the color function from piecewise linear interfaces (called "Front2VOF") is presented, allowing an exact computation of the volume inside a triangulated surface intersecting an arbitrary cubic grid cell. Thus the method is of use within the Front-Tracking method, and is implemented in the PARIS Simulator (http://www.ida.upmc.fr/~zaleski/paris/index.html) code. The computation is independant of direction of integration. Tests are conducted using the oscillating bubble case, and comparisons are done between the Front2VOF algorithm and other methods based on the solution of a Poisson equation.