Preprint 1997-011

A front tracking approach to a two-phase fluid flow model with capillary forces

K. Hvistendahl Karlsen, K.-A. Lie, N. H. Risebro, and J. Frøyen

Abstract: We consider a prototype two-phase fluid flow model with capillary forces. The pressure equation is solved using standard finite 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 diffusion (capillary forces) may change rapidly during a simulation. The corrected splitting is designed so that any combination of advection and diffusion is resolved accurately. It gives a hyperbolic conservation law for modelling advection and a parabolic equation for modelling diffusion. The conservation law is solved by front tracking, which naturally leads to a dynamically defined residual flux term that can be included in the diffusion equation. The residual term ensures that self-sharpening fronts are given the correct structure. A Petrov--Galerkin finite element method is used to solve the diffusion equation. We present several examples that demonstrate potential shortcomings of standard viscous operator splitting and highlights the corrected splitting strategy. This is the first time a front tracking simulator is applied to a flow model including capillary forces.

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A front tracking approach to a two-phase fluid flow model with capillary forces
Kenneth Hvistendahl Karlsen, <>
Knut-Andreas Lie , <>
Nils Henrik Risebro , <>
Johnny Frøyen
Publishing information:
To appear in In Situ
Revised July 11 1997; new version submitted to server.
Submitted by:
<> April 28 1997.
<> July 17 1997.

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