A new formula for the analytical solution of the radial dispersion problem

Water Resources Research
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Abstract

A new formula is presented for the analytical solution of the radial dispersion problem, which analyzes the dispersive transport of a tracer in radial flow from a recharge well. This formula is simpler than a solution presented by previous investigators, but the two solutions are shown to be equivalent. Because the analytical solution consists of an integral of an oscillatory function, it is evaluated as an alternating series, the terms of which are the integrals over successive half cycles of the integrand. An efficient algorithm is used to accelerate convergence of the series. The accuracies of previous solutions obtained by finite difference, numerical Laplace transform, and perturbation methods are examined by comparison with the analytical solution. Numerical values of the solution are tabulated for readers interested in checking the accuracies of solute transport codes.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title A new formula for the analytical solution of the radial dispersion problem
Series title Water Resources Research
DOI 10.1029/WR022i011p01597
Volume 22
Issue 11
Year Published 1986
Language English
Publisher American Geophysical Union
Contributing office(s) Toxic Substances Hydrology Program
Description 9 p.
First page 1597
Last page 1605