Modeling of Flow in Three-Dimensional, Multizone, Anisotropic Porous Media with Weakly Singular Integral Equation Method
Publication: Journal of Engineering Mechanics
Volume 135, Issue 8
Abstract
A symmetric Galerkin boundary element method is developed for modeling steady-state Darcy’s flow in three-dimensional porous media. The proposed technique is capable of treating a nonhomogeneous medium that consists of several regions possessing different permeabilities and may contain a surface of discontinuity such as impermeable seals. The key governing equations are established based on a pair of weakly singular weak-form integral equations for the fluid pressure and the fluid flux. The crucial feature of those integral equations are that they are completely regularized such that all involved kernels are only weakly singular and that they are applicable to a medium possessing generally anisotropic permeability. A final system of governing integral equations is obtained in a symmetric form and validity of all involved integrals only requires continuity of the pressure boundary data; as a consequence, continuous interpolations can be employed everywhere in the numerical approximation. To accurately capture the jump of the fluid pressure in the local region near the boundary of the discontinuity surface, special tip elements are employed. To further enhance accuracy and computational efficiency of the method, special integration quadrature is adopted to treat both weakly singular and nearly singular integrals and an interpolation strategy is utilized to evaluate the kernels for anisotropic permeability. As demonstrated by various numerical experiments, the current method yields highly accurate results with only weak dependence on mesh refinement.
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Acknowledgments
The writer gratefully acknowledges partial support provided by Chulalongkorn University in terms of grants for development of new faculty staff, Ratchadaphiseksomphot Endowment Fund.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 8 • August 2009
Pages: 828 - 838
Copyright
© 2009 ASCE.
History
Received: Dec 18, 2006
Accepted: Mar 24, 2009
Published online: Jul 15, 2009
Published in print: Aug 2009
Notes
Note. Associate Editor: Arif Masud
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