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

Rami Ben-Zvi, Harvey Scher, Shidong Jiang, Brian Berkowitz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)239-263
Number of pages25
JournalTransport in Porous Media
Volume115
Issue number2
DOIs
StatePublished - Nov 1 2016

All Science Journal Classification (ASJC) codes

  • Catalysis
  • Chemical Engineering(all)

Keywords

  • Continuous time random walk
  • Heterogeneous porous media
  • Prony model

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