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The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic

Water Resources Research

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https://doi.org/10.1029/WR022i007p01149

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Abstract

In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

Additional publication details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic
Series title:
Water Resources Research
DOI:
10.1029/WR022i007p01149
Volume:
22
Issue:
7
Year Published:
1986
Language:
English
Publisher:
American Geophysical Union
Description:
6 p.
First page:
1149
Last page:
1154