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ISSN Print: 1099-2391

Archives: Volume 1, 1999 to Volume 4, 2002

# Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v3.i2-3.10
18 pages

## INTEGRAL TRANSFORM SOLUTIONS FOR ONE-DIMENSIONAL TRANSIENT FLOW AND CONTAMINANT TRANSPORT IN DUAL-POROSITY SYSTEMS

Rodrigo P. A. Rocha
Department of Mechanical Engineering—EE/COPPE, Federal University of Rio de Janeiro, CP 68503, Rio de Janeiro, RJ, 21945-970, Brazil
Manuel Ernani C. Cruz
Department of Mechanical Engineering EE/COPPE/Federal University of Rio de Janeiro CP 68503 Rio de Janeiro, Rio de Janeiro, 21945-970 Brazil

Scientific Journal Referee
2008 - 2008 Journal: Energy & Fuels
2007 - 2007 Journal: Brazilian Journal of Chemical Engineering
2006 - 2006 Journal: Journal of Mathematical Sciences
2006 - 2006 Journal: International Journal of Solids and Structures
2005 - 2005 Journal: Science & Engineering
2003 - 2003 Journal: Heat Transfer Engineering
2000 - 2004 Journal: Journal of the Brazilian Society of Mechanical Sciences and Engineering
2001 - 2005 Journal: Applied and Computational Mathematics
2002 - 2007 Journal: International Journal of Thermal Sciences
1999 - 2002 Journal: Proceedings of the Royal Society of London. Mathematical, Physical and Engi
2002 - 2002 Journal: Communications in Numerical Methods in Engineering
2001 - 2001 Journal: Inverse Problems in Engineering
1999 - 2000 Journal: Hybrid Methods in Engineering

### ABSTRACT

In this article, we present a hybrid analytical-numerical solution for the one-dimensional transient problem of flow and contaminant transport in an unsaturated fractured porous medium, modeled as a dual-porosity system. The flow is considered to be Darcian and governed by the Richards equation, and the solute transport is governed by the advection-dispersion equation. Because the governing partial differential equations are coupled and possess advective terms, the classical (analytical) method of integral transformation cannot be applied. Instead, we employ the generalized integral transform technique (GITT), a hybrid method of wide applicability. We consider constant soil properties and Dirichlet boundary conditions for both flow and transport problems. To validate our solution procedure, we obtain pressure head and contaminant concentration results for the limiting case of an ordinary porous medium. The capability of our hybrid approach is demonstrated through the solution and analysis of an example problem.