Modeling of flow in three-dimensional, multizone, anisotropic porous media with weakly singular integral equation method

Journal of Engineering Mechanics

Volumn 135, Issue 8, 2009, Pages 828-838

  Rungamornrat, Jaroon ^a  

^a CHULALONGKORN UNIVERSITY   (Thailand)

Author keywords

Anisotropy; Boundary element method; Darcy's law; Discontinuities; Permeability; Porous media; Steady flow

Indexed keywords

ANISOTROPIC PERMEABILITY; ANISOTROPIC POROUS MEDIA; DARCY'S FLOW; DARCY'S LAW; DISCONTINUITIES; DISCONTINUITY SURFACES; FLUID FLUXES; FLUID PRESSURES; GOVERNING EQUATIONS; LOCAL REGION; MESH REFINEMENT; NEARLY SINGULAR INTEGRAL; NONHOMOGENEOUS MEDIUM; NUMERICAL APPROXIMATIONS; NUMERICAL EXPERIMENTS; PERMEABILITY; POROUS MEDIA; PRESSURE BOUNDARY; SYMMETRIC GALERKIN BOUNDARY ELEMENT METHOD; WEAKLY SINGULAR; WEAKLY SINGULAR INTEGRAL EQUATIONS;

ANISOTROPY; CAPILLARITY; COMPUTATIONAL EFFICIENCY; FLUID DYNAMICS; GROUNDWATER FLOW; INTEGRAL EQUATIONS; INTERPOLATION; POROUS MATERIALS; SEEPAGE; STEADY FLOW; THREE DIMENSIONAL;

BOUNDARY ELEMENT METHOD;

ACCURACY ASSESSMENT; ANISOTROPIC MEDIUM; BOUNDARY ELEMENT METHOD; DARCY LAW; FLUID PRESSURE; GALERKIN METHOD; PERMEABILITY; POROUS MEDIUM; STEADY FLOW; THREE-DIMENSIONAL FLOW;

EID: 68049083721     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(2009)135:8(828)     Document Type: Article

References (32)

1. Bonnet, M. (1995). "Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity." Eng. Anal. Boundary Elem. EABAEL0955-7997, 15, 93-102. 10.1016/ 0955-7997(95)00022-G
2. Brebbia, C. A., and Dominguez, J. (1989). Boundary elements: An introductory course, 2nd Ed., McGraw-Hill, New York.
3. Brezzi, F., Hughes, T. J. R., Marini, L. D., and Masud, A. (2005). "Mixed discontinuous Galerkin methods for Darcy flow." J. Sci. Comput. JSCOEB0885-7474, 22, 119-145. 10.1007/s10915-004-4150-8
4. Deans, S. R. (1983). The radon transform and some of its applications, Wiley, New York.
5. Dominguez, J., Ariza, M. P., and Gallego, R. (2000). "Flux and traction boundary elements without hypersingular or strongly singular integrals." Int. J. Numer. Methods Eng JNMBH0029-5981, 48, 111-135. 10.1002/ (SICI)1097-0207(20000510)48:1<111::AID-NME870>3.0.CO;2-Y
6. Frangi, A., and Maier, G. (2003). "The symmetric Galerkin BEM in linear and non-linear fracture mechanics of zonewise homogeneous solids." Recent advance in boundary element and their solid mechanics applications, D. Beskos, ed., Springer, Berlin, 167-204.
7. Gel'fand, I. M., and Shilov, G. E. (1964). Generalized functions: Properties and operations, Vol. 1, Academic, New York.
8. Gray, L. J., Martha, L. F., and Ingraffea, A. R. (1990). "Hypersingular integrals in boundary element fracture analysis." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 29, 1135-1158. 10.1002/nme.1620290603
9. Gray, L. J., and Paulino, G. H. (1997). "Symmetric Galerkin boundary integral formulation for interface and multi-zone problems." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 40, 3085-3101. 10.1002/ (SICI)1097-0207(19970830)40:16<3085::AID-NME194>3.0.CO;2-U
10. Hayami, K. (1992). "A projection transformation method for nearly singular surface boundary element integrals." Lecture notes in engineering, Vol. 73, C. A. Brebbia, and S. A. Orszag, eds., Springer, Berlin.
11. Hayami, K., and Brebbia, C. A. (1988). "Quadrature methods for singular and nearly singular integrals in 3-D boundary element method." Boundary elements X, Vol. 1, C. A. Brebbia, ed., Springer, Berlin, 237-264.
12. Hayami, K., and Matsumoto, H. (1994). "A numerical quadrature for nearly singular boundary element integrals." Eng. Anal. Boundary Elem. EABAEL0955-7997, 13, 143-154. 10.1016/0955-7997(94)90017-5
13. Helgason, S. (1999). The radon transform, 2nd Ed., Birkhäuser, Boston.
14. Hughes, T. J. R., Masud, A., and Wan, J. (2006). "A discontinuous-Galerkin finite element method for Darcy flow." Comput. Methods Appl. Mech. Eng. CMMECC0045-7825, 195, 3347-3381. 10.1016/j.cma.2005.06.018
15. Jorge, A. B., Ribeiro, G. O., Cruse, T. A., and Fisher, T. S. (2001). "Self-regular boundary integral equation formulations for Laplace's equation in 2-D." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 51, 1-29. 10.1002/nme.138
16. Li, H. B., and Han, G. M. (1985). "A new method for evaluating singular integral in stress analysis of solids by the direct boundary element method." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 21, 2071-2098. 10.1002/nme.1620211109
17. Li, S., and Mear, M. E. (1998). "Singularity-reduced integral equations for displacement discontinuities in three-dimensional linear elastic media." Int. J. Fract. IJFRAP0376-9429, 93, 87-114. 10.1023/ A:1007513307368
18. Li, S., Mear, M. E., and Xiao, L. (1998). "Symmetric weak-form integral equation method for three dimensional fracture analysis." Comput. Methods Appl. Mech. Eng. CMMECC0045-7825, 151, 435-459. 10.1016/ S0045-7825(97)00199-0
19. Liggett, J. A., and Liu, L. F. (1983). The boundary integral equation method for porous media flow, Allen and Unwin, London.
20. Martha, L. F., Gray, L. J., and Ingraffea, A. R. (1992). "Three-dimensional fracture simulation with a single-domain, direct boundary element formulation." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 35, 1907-1921. 10.1002/nme.1620350911
21. Martin, P. A., and Rizzo, F. J. (1996). "Hypersingular integrals: How smooth must the density be?" Int. J. Numer. Methods Eng. IJNMBH0029-5981, 39, 687-704. 10.1002/ (SICI)1097-0207(19960229)39:4<687::AID-NME876>3.0.CO;2-S
22. Masud, A., and Hughes, T. J. R. (2002). "A stabilized mixed finite element method for Darcy flow." Comput. Methods Appl. Mech. Eng. CMMECC0045-7825, 191, 4341-4370. 10.1016/S0045-7825(02)00371-7
23. McLean, W. (2000). Strongly elliptic systems and boundary integral equations, Cambridge University Press, New York.
24. Nagarajan, A., Lutz, E. D., and Mukherjee, S. (1994). "A novel boundary elements method for linear elasticity with no numerical integration for 2D and line integrals for 3D problems." J. Appl. Mech. JAMCAV0021-8936, 61, 264-269. 10.1115/1.2901439
25. Rungamornrat, J. (2006). "Analysis of 3D cracks in anisotropic multi-material domain with weakly singular SGBEM." Eng. Anal. Boundary Elem. EABAEL0955-7997, 30, 834-846. 10.1016/ j.enganabound.2006.05.005
26. Rungamornrat, J., and Mear, M. E. (2008a). "Weakly-singular, weak-form integral equations for cracks in three-dimensional anisotropic media." Int. J. Solids Struct. IJSOAD0020-7683, 45, 1283-1301. 10.1016/j.ijsolstr.2007.09.030
27. Rungamornrat, J., and Mear, M. E. (2008b). "A weakly-singular SGBEM for analysis of cracks in 3D anisotropic media." Comput. Methods Appl. Mech. Eng. CMMECC0045-7825, 197, 4319-4332.
28. Rungamornrat, J., and Wheeler, M. F. (2006a). "Weakly-singular integral equations for steady-state flow in isotropic porous media." Rep. No. 05-30, Institute for Computational Engineering and Sciences, Univ. of Texas at Austin, Austin, Tex.
29. Rungamornrat, J., and Wheeler, M. F. (2006b). "Weakly-singular integral equations for Darcy's flow in anisotropic porous media." Eng. Anal. Boundary Elem. EABAEL0955-7997, 30, 237-246. 10.1016/ j.enganabound.2005.11.003
30. Shiah, Y. C., and Tan, C. L. (2004). "BEM treatment of three-dimensional anisotropic field problems by direct domain mapping." Eng. Anal. Boundary Elem. EABAEL0955-7997, 28, 43-52. 10.1016/S0955-7997(03)00114-0
31. Sutradhar, A., and Paulino, G. H. (2004). "A simple boundary element method for problems of potential in non-homogeneous media." Int. J. Numer. Methods Eng. IJNMBH0029-5981, 60, 2203-2230. 10.1002/ nme.1046
32. Xiao, L. (1998). "Symmetric weak-form integral equation method for three dimensional fracture analysis." Ph.D. dissertation, Univ. of Texas at Austin, Austin, Tex.