HR: 0830h
AN: H21D-0881    [PDF]
TI: Transport by Eigendecomposition
AU: * Purvance, D T
EM: d.purvance@att.net
AF: hydrOhm Environmental Geophysics, 1456 Washington Street, Reno, NV 89503 United States
AB: The Fourier transform of the transport equation is a Fredholm integral equation of the second kind. When expressed as a linear sum, this integral equation becomes a homogeneous system of linear equations whose eigendecomposition determines the eigenvalue frequencies at which eigenvector concentration densities satisfy the transport equation. Corresponding spacetime concentration densities are computed by inverse transforming the linear combination of said eigenvectors that honor some initial condition. This paper finds that the key to a successful inverse transform is to choose length and time scales that prevent phase wrapping at mid transform. A numerical demonstration, treating the problem of predicting the fate of radionuclides invading the groundwaters of Nevada's fractured welded tuffs, is provided. Using the same random fractal flow parameters as was used for the author's previous travel times [WRR 37(12) 2915-2918, 2001], this paper shows that concentration densities derived by eigendecomposition satisfy the transport equation with an average relative error of 3.7 percent. And, in excellent agreement with [WRR 37(12) 2915-2918, 2001] this direct solution also predicts that an impulse radionuclide source entering the groundwaters of Nevada's fractured welded tuffs will on average spread to a 5 km monitoring point in a few centuries.
DE: 1832 Groundwater transport
DE: 3230 Numerical solutions
DE: 3250 Fractals and multifractals
DE: 5139 Transport properties
SC: Hydrology [H]
MN: 2003 Fall Meeting