One-Dimensional Finite Element Method Solution of a Class of Integro-Differential Equations: Application to Non-Fickian Transport in Disordered Media
| Autor: | Harvey Scher, Shidong Jiang, Rami Ben-Zvi, Brian Berkowitz |
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| Rok vydání: | 2016 |
| Předmět: |
Recurrence relation
Linear element Laplace transform Discretization Differential equation General Chemical Engineering 0208 environmental biotechnology Mathematical analysis 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Catalysis Finite element method 020801 environmental engineering Time domain 0101 mathematics Continuous-time random walk Mathematics |
| Zdroj: | Transport in Porous Media. 115:239-263 |
| ISSN: | 1573-1634 0169-3913 |
| DOI: | 10.1007/s11242-016-0712-0 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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