ARS | Publication request: Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique

Submitted to: International Journal of Heat and Mass Transfer
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: January 13, 2009
Publication Date: March 11, 2009
Repository URL: http://www.ars.usda.gov/SP2UserFiles/Place/53102000/pdf_pubs/P2278.pdf
Citation: Perez-Guerrero, J.S., Pimentel, L.G., Skaggs, T.H., Van Genuchten, M.T. 2009. Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique. International Journal of Heat and Mass Transfer. 52:3297-3304.

Interpretive Summary: Mathematical models of chemical transport processes are frequently used to investigate and manage a variety of environmental and agricultural systems. For example, mathematical models may be used to predict how fast contaminants will move through soils and groundwater. Mathematical models generally take the form of differential equations which must be solved in order to make predictions. In this work, we developed a new solution procedure that is superior to ones that have been used in the past. The work will be of interest to scientists and engineers who use mathematical models to study chemical transport in the environment.

Technical Abstract: This paper presents a formal exact solution of the linear advection-diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection-diffusion equation into an exclusively diffusive equation. The new diffusive problem is solved analytically using the classic version of Generalized Integral Transform Technique (GITT), resulting in an explicit formal solution. The new solution is shown to converge faster than a hybrid analytical-numerical solution previously obtained by applying the GITT directly to the advection-diffusion transport equation.