A Front{tracking Approach to a Two-phase Fluid{flow Model with Capillary Forces

We consider a prototype two-phase uid-ow model with capillary forces. The pressure equation is solved using standard nite-elements and multigrid techniques. The parabolic saturation equation is addressed via a novel corrected operator splitting approach. In typical applications, the importance of advection versus diiusion (capillary forces) may change rapidly during a simulation. The corrected splitting is designed so that any combination of advection and diiusion is resolved accurately. It gives a hyperbolic conservation law for modelling advection and a parabolic equation for modelling diiusion. The conservation law is solved by front tracking, which naturally leads to a dynamically deened residual ux term that can be included in the diiusion equation. The residual term ensures that self-sharpening fronts are given the correct structure. A Petrov{Galerkin nite-element method is used to solve the diiusion equation. We present several examples that demonstrate potential shortcomings of standard viscous operator splitting and highlight the corrected splitting strategy. This is the rst time a front-tracking simulator is applied to a ow model including capillary forces.