One-Dimensional Finite Element Method Solution of a Class of Integro-Differential Equations: Application to Non-Fickian Transport in Disordered Media

Document Type

Article

Publication Date

11-1-2016

Abstract

We study an integro-differential equation that has important applications to problems of anomalous transport in highly disordered media. In one application, the equation is the continuum limit of a continuous time random walk used to quantify non-Fickian (anomalous) contaminant transport. The finite element method is used for the spatial discretization of this equation, with an implicit scheme for its time discretization. To avoid storage of the entire history, an efficient sum-of-exponential approximation of the kernel function is constructed that allows a simple recurrence relation. A 1D formulation with a linear element is implemented to demonstrate this approach, by comparison with available experiments and with an exact solution in the Laplace domain, transformed numerically to the time domain. The proposed scheme convergence assessment is briefly addressed. Future extensions of this implementation are then outlined.

Identifier

85013868014 (Scopus)

Publication Title

Transport in Porous Media

External Full Text Location

https://doi.org/10.1007/s11242-016-0712-0

e-ISSN

15731634

ISSN

01693913

First Page

239

Last Page

263

Issue

2

Volume

115

Grant

1418918

Fund Ref

National Science Foundation

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