Premium
Two‐dimensional finite element method solution of a class of integro‐differential equations: Application to non‐Fickian transport in disordered media
Author(s) -
BenZvi Rami,
Scher Harvey,
Berkowitz Brian
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5524
Subject(s) - finite element method , mathematics , laplace transform , mathematical analysis , solver , kernel (algebra) , exponential function , volterra integral equation , galerkin method , integral equation , mathematical optimization , physics , combinatorics , thermodynamics
Summary A finite element method is developed to solve a class of integro‐differential equations and demonstrated for the important specific problem of non‐Fickian contaminant transport in disordered porous media. This transient transport equation, derived from a continuous time random walk approach, includes a memory function. An integral element is the incorporation of the well‐known sum‐of‐exponential approximation of the kernel function, which allows a simple recurrence relation rather than storage of the entire history. A two‐dimensional linear element is implemented, including a streamline upwind Petrov–Galerkin weighting scheme. The developed solver is compared with an analytical solution in the Laplace domain, transformed numerically to the time domain, followed by a concise convergence assessment. The analysis shows the power and potential of the method developed here. Copyright © 2017 John Wiley & Sons, Ltd.