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Title: On the anisotropic advection-diffusion equation with time dependent coefficients

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. Here, 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 specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media
 [1] ;  [2] ;  [3]
  1. UNAM (Mexico)
  2. Instituto Mexicano de Petroleo (Mexico)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Revista Mexicana de Fisica
Additional Journal Information:
Journal Volume: 63; Journal Issue: 1; Journal ID: ISSN 0035-001X
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
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; time-dependent diffusion; anisotropic media; tracer and pollutant transport
OSTI Identifier: