Result: Theory of diffusions applied to stochastic flow in porous media

Title:
Theory of diffusions applied to stochastic flow in porous media
Authors:
VERWOERD, W. S, KULASIRI, D
Source:
Stochastic models in engineering, technology, and managementMathematical and computer modelling. 38(11-13):1453-1459
Publisher Information:
Oxford: Elsevier Science, 2003.
Publication Year:
2003
Physical Description:
print, 11 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Physique, Physics, Domaines classiques de la physique (y compris les applications), Fundamental areas of phenomenology (including applications), Mécanique des fluides, Fluid dynamics, Ecoulements non homogènes, Nonhomogeneous flows, Ecoulements en milieu poreux, Flows through porous media, Approche déterministe, Deterministic approach, Enfoque determinista, Ecoulement milieu poreux, Porous medium flow, Equation diffusion, Diffusion equation, Ecuación difusión, Equation différentielle, Differential equations, Equation intégrale, Integral equations, Equation stochastique, Stochastic equation, Ecuación estocástica, Equation transport, Transport equation, Ecuación transporte, Fonction répartition, Distribution function, Función distribución, Hydrodynamique, Hydrodynamics, Intégrale, Integrals, Loi probabilité, Probability distribution, Ley probabilidad, Milieu poreux, Porous medium, Medio poroso, Processus diffusion, Diffusion process, Proceso difusión, 65C30, Equation d&éterministe, Deterministic equation, Formule Dynkin, Dynkin formula
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Applied Computation, Mathematics and Statistics Group, Lincoln University, Canterbury, New Zealand
ISSN:
0895-7177
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=15368223
Rights:
Copyright 2004 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Physics: fluid mechanics
Accession Number:
edscal.15368223
Database:
PASCAL Archive

Further Information

Contaminant transport by liquid flow in a porous medium is modeled by the addition of a stochastic term to Darcy's flow equation. The resulting stochastic differential equation is studied using results from the theory of diffusions as embodied in the Dynkin formula. The resulting integral equation for the probability distribution of fluid elements is solved for the case of a spatially homogeneous medium without microdiffusion. This distribution is shown to also solve a deterministic transport equation containing an effective diffusion constant, analogous to the hydrodynamic dispersion equation. This relates the stochastic and deterministic approaches to the contaminant transport problem. The case of a nonhomogeneous medium is discussed, leading to a tentative conclusion that the stochastic description will not reduce to a dispersion equation in general.