On the anisotropic advectiondiffusion equation with time dependent coefficients
The advectiondiffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its nonclassical transport features and to the use of a nonorthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the timedependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on powerlaw correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media
 Authors:

^{[1]};
^{[2]};
^{[3]}
 UNAM (Mexico)
 Instituto Mexicano de Petroleo (Mexico)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Revista Mexicana de Fisica
 Additional Journal Information:
 Journal Volume: 63; Journal Issue: 1; Journal ID: ISSN 0035001X
 Publisher:
 Sociedad Mexicana de Physica
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; timedependent diffusion; anisotropic media; tracer and pollutant transport
 OSTI Identifier:
 1333060
HernandezCoronado, Hector, Coronado, Manuel, and DelCastilloNegrete, Diego B. On the anisotropic advectiondiffusion equation with time dependent coefficients. United States: N. p.,
Web.
HernandezCoronado, Hector, Coronado, Manuel, & DelCastilloNegrete, Diego B. On the anisotropic advectiondiffusion equation with time dependent coefficients. United States.
HernandezCoronado, Hector, Coronado, Manuel, and DelCastilloNegrete, Diego B. 2017.
"On the anisotropic advectiondiffusion equation with time dependent coefficients". United States.
doi:. https://www.osti.gov/servlets/purl/1333060.
@article{osti_1333060,
title = {On the anisotropic advectiondiffusion equation with time dependent coefficients},
author = {HernandezCoronado, Hector and Coronado, Manuel and DelCastilloNegrete, Diego B.},
abstractNote = {The advectiondiffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its nonclassical transport features and to the use of a nonorthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the timedependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on powerlaw correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media},
doi = {},
journal = {Revista Mexicana de Fisica},
number = 1,
volume = 63,
place = {United States},
year = {2017},
month = {2}
}