Abstract
Abstract. A coupled boundary element-finite element procedure, namely, the Green element method (GEM) is applied to the solution of mass transport in heterogeneous media. An equivalent integral equation of the governing differential equation is obtained by invoking the Green's second identity, and in a typical finite element fashion, the resulting equation is solved on each generic element of the problem domain. What is essentially unique about this procedure is the recognition of the particular advantages and particular features possessed by the two techniques and their effective use for the solution of engineering problems.
By utilizing this approach, we observe that the range of applicability of the boundary integral methods is enhanced to cope with problems involving media heterogeneity in a straightforward and realistic manner. The method has been used to investigate problems involving various functional forms of heterogeneity, including head variations in a stream-heterogeneous aquifer interaction and in all these cases encouraging results are obtained without much difficulty.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brady, B. H. G. and Wassyng, A. A.: 1981, A coupled boundary element finite element method for stress analysis, Int. J. Rock Mech. Min. Sci. 16, 235–244.
Cheng, A. H.-D., Antes, H. and Ortner, N.: 1994, Fundamental sollutions of products of Helmhotz and polyharmonic operators engineering analysis with boundary elements.
Cheng, A. H.-D.: 1984, Darcy's flow with variable permeability: A boundary integral solution, Water Resour. Res. 20, 980–984.
Crotty, J. M.: 1982, A block equation solver for large unsymmetric matrices arising in the boundary integral equation method, Int. J. Num. Meth. Eng. 38, 2241–2263.
Ellsworth, D. A.: 1987, Boundary element-finite element procedure for porous and fractured media flow, Water Resour. Res. 23, 551–560.
Harrouni, K. et al.: 1992, Dual reciprocity boundary element method for heterogeneous porous media, in: C. A. Brebbia, et al. (eds), Boundary Element Technology VII, CMP/Elsevier, Amsterdam, pp. 151–159.
Krishnamurthy, T. and Raju, I. S.: 1993, Coupling finite element and boundary element methods for two-dimensional potential problems, Int. J. Num. Meth. Eng. 36, 3395–3616.
Lafe, O. E., Liggett, J. A. and Liu, P.L.-F: 1981, BIEM solutions to contributions of leaky confined, unconfined nonisotropic aquifers, Water Resour. Res. 17, 1431–1444.
Onyejekwe, O. O.: 1996, Green element description of mass transfer in reacting systems, Numerical Heat Transfer Part B 30, 483–498.
Onyejekwe, O. O.: 1997, Green element treatment of Isothermal flow with second order reaction, Int. Comm. Heat Mass Trans. 24, 251–264.
Taigbenu, A. E.: 1995, The Green element method, Int. J. Num. Meth. Eng. 38, 2241–2263.
Taigbenu, A. E. and Onyejekwe, O. O.: 1995, Green element simulations of the transient nonlinear unsaturated flow equation, Appl. Math. Model. 19, 675–684.
Zienkiewicz, O. C., Kelly, D. W. and Pettes, P.: 1977, The coupling of finite element method and boundary solution procedures, Int. J. Num. Meth. Eng. 355–375.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Onyejekwe, O.O. A Boundary Element-Finite Element Equation Solutions to Flow in Heterogeneous Porous Media. Transport in Porous Media 31, 293–312 (1998). https://doi.org/10.1023/A:1006529122626
Issue Date:
DOI: https://doi.org/10.1023/A:1006529122626