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Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Zhuang, Pinghui, Gu, YuanTong, Liu, Fawang, Turner, Ian, & Yarlagadda, Prasad K. (2011) Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method. International Journal for Numerical Methods in Engineering.

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Abstract

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Impact and interest:

11 citations in Scopus
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9 citations in Web of Science®

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ID Code: 45619
Item Type: Journal Article
Additional Information: Early View (Online Version of Record published before inclusion in an issue)
Keywords: Fractional partial differential equation, Fractional advection-diffusion equation, Moving least squares, Meshless method, Meshfree method
DOI: 10.1002/nme.3223
ISSN: 0029-5981
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Current > Schools > School of Curriculum
Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Schools > School of Exercise & Nutrition Sciences
Copyright Owner: Copyright 2011 John Wiley & Sons
Deposited On: 31 Aug 2011 08:51
Last Modified: 26 Mar 2013 09:24

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