| Abstract: | 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 fully deforming grid scheme, which explicitly tracks the location of the filling front, and (2) a fixed grid scheme, that employs an 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. |
