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.


Paper:
Available as PostScript (1.0 Mbytes) or as gzipped PostScript (296 Kbytes; uncompress using gunzip).
Title:
A front tracking approach to a two-phase fluid flow model with capillary forces
Author(s):
Kenneth Hvistendahl Karlsen, mailto:kennethk@mi.uib.no
Knut-Andreas Lie , mailto:andreas@math.ntnu.no
Nils Henrik Risebro , mailto:nilshr@math.uio.no
Johnny Frøyen
Publishing information:
To appear in In Situ
Comments:
Revised July 11 1997; new version submitted to server.
Submitted by:
mailto:kennethk@mi.uib.no April 28 1997.
mailto:andreas@math.ntnu.no July 17 1997.


[ 1996 Preprints | 1997 Preprints | All Preprints | Preprint Server Homepage ]
(c) The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

mailto:conservation@math.ntnu.no
Last modified: Thu Jul 17 11:46:35 1997
Сайт управляется системой uCoz