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Convergent Radial Dispersion: A Note on Evaluation of the Laplace Transform Solution
Author(s) -
Moench Allen F.
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr02301
Subject(s) - laplace transform , dimensionless quantity , péclet number , inverse laplace transform , laplace transform applied to differential equations , mathematical analysis , mathematics , dispersion (optics) , two sided laplace transform , inversion (geology) , impulse response , integral transform , mathematical optimization , mechanics , physics , geology , fourier transform , fourier analysis , fractional fourier transform , optics , paleontology , structural basin
A numerical inversion algorithm for Laplace transforms that is capable of handling rapid changes in the computed function is applied to the Laplace transform solution to the problem of convergent radial dispersion in a homogeneous aquifer. Prior attempts by the author to invert this solution were unsuccessful for highly advective systems where the Peclet number was relatively large. The algorithm used in this note allows for rapid and accurate inversion of the solution for all Peclet numbers of practical interest, and beyond. Dimensionless breakthrough curves are illustrated for tracer input in the form of a step function, a Dirac impulse, or a rectangular input.