Prediction of filling times of porous cavities

A recently proposed implicit scheme for tracking the filling front during liquid impregnation into porous moulds is extended to provide One-shot' predictions for the time to completely fill the mould and the location of the last point to fill. With general boundary conditions applied at the filling gates, it is shown that the time to fill and the location of the last point to fill can be predicted on solving, at most, two linear systems of equations (of size determined by the spatial discretization). This result is confirmed by numerical filling experiments that show, for a variety of mould cavities, that One-shot' solutions agree exactly with filling time and location predictions obtained with multi-time-step simulations.