Weakly singular integral equations for Darcy's flow in anisotropic porous media

Engineering Analysis with Boundary Elements

Volumn 30, Issue 4, 2006, Pages 237-246

  Rungamornrat, Jaroon ^a   Wheeler, Mary F ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Anisotropic permeability; Boundary elements; Darcy's flow; Integral equations; SGBEM; Steady state flow; Weakly singular

Indexed keywords

ANISOTROPY; FLUID DYNAMICS; HYDRAULIC CONDUCTIVITY; INTEGRAL EQUATIONS; RADON; STEADY FLOW;

DARCY'S FLOW; KERNELS; REGULARIZATION PROCEDURE; STOKES' THEOREM; SYMMETRIC GALERKIN BOUNDARY ELEMENT METHOD (SGBEM);

POROUS MATERIALS;

EID: 33644895452     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2005.11.003     Document Type: Article

References (26)

1. G.E. Blandford, A.R. Ingraffea, and J.A. Liggett Two-dimensional stress intensity factor computation using boundary element method Int J Numer Methods Eng 17 1981 387 440
2. M. Bonnet Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity Eng Anal Bound Elem 15 1995 93 102
3. C.A. Brebbia, and J. Dominguez Boundary elements: an introductory course 2nd ed 1989 McGraw-Hill New York
4. S.R. Deans The radon transform and some of its applications 1983 Wiley New York
5. J. Dominguez, M.P. Ariza, and R. Gallego Flux and traction boundary elements without hypersingular or strongly singular integrals Int J Numer Methods Eng 48 2000 111 135
6. A. Frangi Regularization of boundary element formulations by the derivative transfer method, in singular integrals in the boundary element method 1998. Computational Publishers p. 125-64 [chapter 4]
7. I.M. Gel'fand, M.I. Graev, and N.Ya. Vilenkin Generalized functions: integral geometry and representation theory vol. 5 1966 Academic Press New York
8. I.M. Gel'fand, and G.E. Shilov Generalized functions: properties and operations vol. 1 1964 Academic Press New York
9. L.J. Gray, L.F. Martha, and A.R. Ingraffea Hypersingular integrals in boundary element analysis Int J Numer Methods Eng 39 1990 387 404
10. S. Helgason The radon transform 2nd ed 1999 Birkhauser Boston
11. A.B. Jorge, G.O. Ribeiro, T.A. Cruse, and T.S. Fisher Self-regular boundary integral equation formulations for laplace's equation in 2-D Int J Numer Methods Eng 51 2001 1 29
12. S. Li, and M.E. Mear Singularity-reduced integral equations for displacement discontinuities in three-dimensional linear elastic media Int J Fract 93 1998 87 114
13. S. Li, M.E. Mear, and L. Xiao Symmetric weak-form integral equation method for three dimensional fracture analysis Comput Methods Appl Mech Eng 151 1998 435 459
14. J.A. Liggett, and L.-F. Liu The boundary integral equation method for porous media flow 1983 Allen and Unwin London
15. P.A. Martin, and F.J. Rizzo Hypersingular integrals: how smooth must the density be? Int J Numer Methods Eng 39 1996 687 704
16. W. McLean Strongly elliptic systems and boundary integral equations 2000 Cambridge University Press New York
17. A. Nagarajan, E.D. Lutz, and S. Mukherjee A novel boundary elements method for linear elasticity with no numerical integration for 2D and line integrals for 3D problems J Appl Mech 61 1994 264 269
18. Rungamornrat J. A computational procedure for analysis of fracture in three dimensional anisotropic media. PhD Dissertation. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin; 2004.
19. Rungamornrat J, Mear ME. SGBEM for analysis of fracture in 3D anisotropic media. Proceedings of the 16th Eng. Mechanics Conference, ASCE, Seattle; 2003.
20. Rungamornrat J, Mear ME. Weakly-singular, weak-form integral equations for cracks in three-dimensional anisotropic media. Technical Report: ICES Report 05-24. Institute for Computational Engineering and Sciences, The University of Texas at Austin, Texas, USA; June 2005.
21. Rungamornrat J, Wheeler MF. Weakly-singular integral equations for steady-state flow in isotropic porous media. Technical Report: ICES Report 05-30. Institute for Computational Engineering and Sciences, The University of Texas at Austin, Texas, USA; July 2005.
22. A. Sáez, M.P. Ariza, and J. Dominguez Three-dimensional fracture analysis in transversely isotropic solids Eng Anal Bound Elem 20 1997 287 298
23. M.A. Sales, and L.J. Gray Evolution of the anisotropic green's function and its derivatives Comput Struct 69 1998 247 254
24. Y.C. Shiah, and C.L. Tan BEM treatment of three-dimensional anisotropic field problems by direct domain mapping Eng Anal Bound Elem 28 2004 43 52
25. A. Sutradhar, and G.H. Paulino A simple boundary element method for problems of potential in non-homogeneous media Int J Numer Methods Eng 60 2004 2203 2230
26. Xiao L. Symmetric weak-form integral equation method for three dimensional fracture analysis. PhD Dissertation. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin; 1998.