Hybrid Methods in Engineering Modeling, Programming, Analysis, Animation

ISSN for PRINT: 1099-2391

For Online Access

Best Paper Award Selection - Editorial Board Site

2002, Volume4

Issue 1&2

126 pages

Issue price - $250.00

Renato M. Cotta
Universidade Federal do Rio de Janeiro

Mikhail D. Mikhailov
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.

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