An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies

作者：Mohammadnejad T; Khoei A R^*

来源：Computational Mechanics, 2013, 51(3): 327-345.

DOI：10.1007/s00466-012-0732-8

• Partially saturated porous medium
• Two-phase fluid flow
• Fully coupled model
• Extended finite element method
• Weak discontinuity
• Convergence analysis

In this paper, a numerical model is developed for the fully coupled analysis of deforming porous media containing weak discontinuities which interact with the flow of two immiscible, compressible wetting and non-wetting pore fluids. The governing equations involving the coupled solid skeleton deformation and two-phase fluid flow in partially saturated porous media are derived within the framework of the generalized Biot theory. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three-phase formulation. The other variables are incorporated into the model via the experimentally determined functions that specify the relationship between the hydraulic properties of the porous medium, i.e. saturation, permeability and capillary pressure. The spatial discretization by making use of the extended finite element method (XFEM) and the time domain discretization by employing the generalized Newmark scheme yield the final system of fully coupled non-linear equations, which is solved using an iterative solution procedure. Numerical convergence analysis is carried out to study the approximation error and convergence rate of several enrichment strategies for bimaterial multiphase problems exhibiting a weak discontinuity in the displacement field across the material interface. It is confirmed that the problems which arise in the blending elements can have a significant effect on the accuracy and convergence rate of the solution.

• 出版日期2013-3