TY - GEN
T1 - A meshfree method for the fractional advection-diffusion equation
AU - Lian, Yanping
AU - Wagner, Gregory J.
AU - Liu, Wing Kam
N1 - Funding Information:
The support of ARO grant W911NF-15-1-0569 is gratefully acknowledged. Yanping Lian is grateful for the support by the Office of China Postdoctoral Council under the International Postdoctoral Exchange Fellowship Program 2014, and would like to acknowledge Miguel Bessa for his helpful suggestions concerning this contribution.
Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - “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.
AB - “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.
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U2 - 10.1007/978-3-319-51954-8_4
DO - 10.1007/978-3-319-51954-8_4
M3 - Conference contribution
AN - SCOPUS:85018698771
SN - 9783319519531
T3 - Lecture Notes in Computational Science and Engineering
SP - 53
EP - 66
BT - Meshfree Methods for Partial Differential Equations VIII
A2 - Griebel, Michael
A2 - Schweitzer, Marc Alexander
PB - Springer Verlag
T2 - 8th International Workshop on Meshfree Methods for Partial Differential Equations, 2015
Y2 - 7 September 2015 through 9 September 2015
ER -