On upscaling operator-stable Levy motions in fractal porous media

Journal Article · Fri Sep 01 04:00:00 EDT 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2006.01.027· OSTI ID:20840340

Park, Moongyu ^[1]; Cushman, John H ^[1]

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1. Department of Earth and Atmospheric Sciences and Department of Mathematics, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907 (United States)

The dynamics of motile particles, such as microbes, in random porous media are modeled with a hierarchical set of stochastic differential equations which correspond to micro, meso and macro scales. On the microscale the motile particle is modeled as an operator stable Levy process with stationary, ergodic, Markov drift. The micro to meso and meso to macro scale homogenization is handled with generalized central limit theorems. On the mesoscale the Lagrangian drift (or the Lagrangian acceleration) is assumed Levy to account for the fractal character of many natural porous systems. Diffusion on the mesoscale is a result of the microscale asymptotics while diffusion on the macroscale results from the mesoscale asymptotics. Renormalized Fokker-Planck equations with time dependent dispersion tensors and fractional derivatives are presented at the macro scale.

• OSTI ID: 20840340
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 217; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
DISPERSIONS
FOKKER-PLANCK EQUATION
FRACTALS
LAGRANGIAN FUNCTION
MARKOV PROCESS
PARTICLES
POROUS MATERIALS
RANDOMNESS
TENSORS
TIME DEPENDENCE