Exact series solutions of reactive transport models with general initial conditions

Simpson, Matthew & Ellery, Adam (2014) Exact series solutions of reactive transport models with general initial conditions. Journal of Hydrology, 513, pp. 7-12.

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Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

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4 citations in Scopus
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3 citations in Web of Science®

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ID Code: 68771
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Reactive transport, Laplace transform, Maclaurin series, Power series
DOI: 10.1016/j.jhydrol.2014.03.035
ISSN: 0022-1694
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Elsevier
Deposited On: 19 Mar 2014 22:40
Last Modified: 07 Jun 2016 04:15

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