Numerical solution of transient, free surface problems in porous media

The focus of this paper is the development of numerical schemes for tracking the moving fluid surface during the filling of a porous medium (e.g., polymer injection into a porous mold cavity). Performing a mass balance calculation on an arbitrarily deforming control volume, leads to a general governing filling equation. From this equation, a general, fully time implicit, numerical scheme based on a finite volume space discretization is derived. Two numerical schemes are developed: (1) a fatty deforming grid scheme, which explicitly tracks the location of the filling front, and (2) a fixed grid scheme, that employs in auxiliary variable to locate the front. The validity of the two schemes is demonstrated by solving a variety of one- and two-dimensional problems: both approaches provide predictions with similar accuracy and agree well with available analytical solutions.