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This paper focuses on adaptive finite element (FE)‐methods for computation of the motion of viscous fluid interfaces fundamentally encountered in multiphase flow problems in porous media. An interface capturing technique (ICT)‐procedure is formulated with a stabilized finite element scheme in a Eulerian framework to solve the two‐dimensional (2D) and three‐dimensional (3D) Navier–Stokes equation in porous media. Global mesh refinements of the discretized domain and local mesh refinements in the vicinity of the interface are used for the spatial discretization. The ICT is embedded into the finite element scheme by adding an extra advection equation and an additional unbounded degree of freedom to the number of the unknowns. Problems of non‐linear free surface seepage flow in earth‐fill dams are simulated in order to validate the performance of the FE‐ICT. Computations for steady non‐linear seepage flows in 2D and 3D are obtained for homogenous, isotropic and isothermal porous media.
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Sharif et al. (2002) studied this question.
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