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Hybrid Methods in Engineering

ISSN Imprimir: 1099-2391
ISSN On-line: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v4.i1-2.40
27 pages


Renato M. Cotta
Laboratory of Nano- and Microfluidics and Microsystems, LabMEMS, Mechanical Engineering Department and Nanotechnology Engineering Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, Cx. Postal 68503, Rio de Janeiro, RJ, CEP 21945-970, Brazil; Interdisciplinary Nucleus for Social Development—NIDES/CT, UFRJ, Brazil; Mechanical Engineering Department, University College London, UCL, United Kingdom
Mikhail D. Mikhailov
Applied Mathematics Center, PO Box 384, Sofia, Technical University, Sofia, Bulgaria; and Mechanical Engineering Department—EE/COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68.503, Rio de Janeiro, RJ, 21945-970, Brasil
M. Ungs
Tetra Tech, Inc., 3746 Mt. Diablo Blvd., Ste.300, Lafayette, CA 94549-3681, USA


Hybrid numerical-analytical solutions for contaminant transport in porous media with parallel fractures are obtained employing the Mathematica platform. The proposed model involves the transient convection-diffusion equation for dispersion within the fractures, coupled to the symmetric transversal diffusion into the adjacent porous matrix along the fracture's length. The Laplace transform approach is employed to transform the original governing partial differential equations. The resulting transformed ordinary differential equations are analytically solved to yield symbolic expressions that are numerically inverted through classic schemes for Laplace transform inversion. In addition, an improved lumped approach is applied to the porous matrix diffusion equation, yielding simplified coupled partial differential formulations, which are solved through the same numerical-analytical scheme. The proposed hybrid solution is first validated against previously reported analytical solutions and critically analyzed in terms of convergence behavior. The article is presented in the Mathematica notebook format, to more accurately illustrate the symbolic computation steps and to demonstrate the capabilities of this simulation tool.