A two dimensional numerical study of viscous fingering in a porous medium

In this paper, a two dimensional numerical study of viscous fingering in a porous medium is presented. A two-phase Newtonian fluid flow at low Reynolds numbers is considered. Surface tension between the two fluids is accounted for by use of the Young-Laplace equation. A direct boundary integral formulation is used for the basis of the numerical method with C1 continuous elements used for discretization. A number of time stepping and re-meshing strategies is discussed. Viscous fingering is studied as a function of the relative viscosity of the two fluids, the porosity of the formation, and the interfacial surface tension. It is found that re-meshing schemes must be used to obtain stable evolution of the interface and accurate results.