A GIF-based Stochastic Boundary Element Method for Random Porous Media
Using a global interpolation function (GIF) approach, boundary element solutions are obtained for flows in porous media with random hydraulic conductivity. The formulation is based on the indirect approach. The solution field is decomposed into two parts. The first is due to the influence of the constant (or effective) property of the medium. This is represented by a boundary integral term. The second, which is due solely to the random nature of the permeability, is represented by a series of bases functions. Appropriate expressions are obtained for the statistics of the primary flow variables (hydraulic head and flux) in terms of the statistics of the permeability field. Numerical implementations include the use of different families of orthogonal trigonometric, polynomial, and wavelet bases functions. The ensuing code can be used for both the forward solution (i.e., determination of flow field) and the inverse solution (e.g., identification of parameters).
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- 3.Cheng, A. H-D., and O.E. Lafe, Boundary Element Solution for Stochastic Groundwater Flow: Random Boundary Condition and Recharge, Water Resour. Res. 27, 1991.Google Scholar
- 4.Cheng, A. H-D., Y. Abousleiman, F. Ruan, O.E. Lafe, Boundary Element Solution for Stochastic Groundwater Flow: Temporal Weakly Stationary Problems, Water Resour. Res., 29(8). 1993.Google Scholar
- 5.Cheng, A. H-D., S. Grilli, and O. Lafe, Dual Reciprocity Boundary Element Based on Global Interpolation Functions, Eng. Analysis with Boundary Elements, 13, 1994.Google Scholar
- 6.Lafe, O.E., and A. H-D. Cheng, A Stochastic Boundary Element Method for Groundwater Flow with Random Boundary Conditions and Recharge, Boundary Element techniques: Applications in Engineering, Proceedings of BETECH90 Conference, Windsor, canada, eds. C/A. Brebbia, and N.G. Zamani, pp. 271 – 280, June 6–8, 1989.Google Scholar
- 7.Lafe, O.E., and A. H-D. Cheng, Stochastic Analysis of Groundwater Flow, in Computational Water Resources, eds. D. Benasari, C.A. Brebbia & D. Ouazar, Computational Mechanics Publication. Southampton, Boston, 1991.Google Scholar
- 8.Lafe, O., and A. H-D. Cheng, Stochastic Indirect Boundary Element Method, in Computational Stochastic Mechanics, eds. A. H-D. Cheng and C.Y. Yang, Comp. Mech. Pub., pp. 301–319, 1993.Google Scholar
- 9.Lafe, O., A Dual Reciprocal Boundary element Formulation for Viscous Flows, in Proc. NASA Fifth Annual Thermal and Fluids Analysis Workshop (NASA Conference Publication 10122), Brook Park, Aug. 16–20, 1993.Google Scholar