On the anisotropic advection-diffusion equation with time dependent coefficients
Abstract The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal 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 time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. We discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ∼ t, a second case specifically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media.
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Sociedad Mexicana de Física
2017
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oai:scielo:S0035-001X20170001000402018-11-06On the anisotropic advection-diffusion equation with time dependent coefficientsHernandez-Coronado,H.Coronado,M.Castillo-Negrete,D. Del- Time-dependent diffusion anisotropic media tracer and pollutant transport Abstract The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal 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 time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. We discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ∼ t, a second case specifically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media.info:eu-repo/semantics/openAccessSociedad Mexicana de FísicaRevista mexicana de física v.63 n.1 20172017-02-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2017000100040en |
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Hernandez-Coronado,H. Coronado,M. Castillo-Negrete,D. Del- |
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Hernandez-Coronado,H. Coronado,M. Castillo-Negrete,D. Del- On the anisotropic advection-diffusion equation with time dependent coefficients |
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Hernandez-Coronado,H. Coronado,M. Castillo-Negrete,D. Del- |
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Hernandez-Coronado,H. |
title |
On the anisotropic advection-diffusion equation with time dependent coefficients |
title_short |
On the anisotropic advection-diffusion equation with time dependent coefficients |
title_full |
On the anisotropic advection-diffusion equation with time dependent coefficients |
title_fullStr |
On the anisotropic advection-diffusion equation with time dependent coefficients |
title_full_unstemmed |
On the anisotropic advection-diffusion equation with time dependent coefficients |
title_sort |
on the anisotropic advection-diffusion equation with time dependent coefficients |
description |
Abstract The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal 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 time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. We discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ∼ t, a second case specifically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media. |
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Sociedad Mexicana de Física |
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2017 |
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http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2017000100040 |
work_keys_str_mv |
AT hernandezcoronadoh ontheanisotropicadvectiondiffusionequationwithtimedependentcoefficients AT coronadom ontheanisotropicadvectiondiffusionequationwithtimedependentcoefficients AT castillonegreteddel ontheanisotropicadvectiondiffusionequationwithtimedependentcoefficients |
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