A meshfree method for the fractional advection-diffusion equation

Yanping Lian, Gregory J Wagner, Wing K Liu*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

“Non-local” phenomena are common to problems involving strong heterogeneity, fracticality, or statistical correlations. A variety of temporal and/or spatial fractional partial differential equations have been used in the last two decades to describe different problems such as turbulent flow, contaminant transport in ground water, solute transport in porous media, and viscoelasticity in polymer materials. The study presented herein is focused on the numerical solution of spatial fractional advection-diffusion equations (FADEs) via the reproducing kernel particle method (RKPM), providing a framework for the numerical discretization of spacial FADEs. However, our investigation found that an alternative formula of the Caputo fractional derivative should be used when adopting Gauss quadrature to integrate equations with fractional derivatives. Several one-dimensional examples were devised to demonstrate the effectiveness and accuracy of the RKPM and the alternative formula.

Original languageEnglish (US)
Title of host publicationMeshfree Methods for Partial Differential Equations VIII
PublisherSpringer Verlag
Pages53-66
Number of pages14
Volume115
ISBN (Print)9783319519531
DOIs
StatePublished - Jan 1 2017
Event8th International Workshop on Meshfree Methods for Partial Differential Equations, 2015 - Bonn, Germany
Duration: Sep 7 2015Sep 9 2015

Publication series

NameLecture Notes in Computational Science and Engineering
Volume115
ISSN (Print)1439-7358

Other

Other8th International Workshop on Meshfree Methods for Partial Differential Equations, 2015
CountryGermany
City Bonn
Period9/7/159/9/15

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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