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Stability and Convergence of Implicit Numerical Methods for a Class of Fractional Advection-Dispersion Models

[+] Author Affiliations
Fawang Liu

Queensland University of Technology, Brisbane, QLD, Australia

Pinghui Zhuang

Xiamen University, Xiamen, Fujian, China

Kevin Burrage

Queensland University of Technology, Brisbane, QLD, Australia; Oxford University, Oxford, UK

Paper No. DETC2011-47071, pp. 85-94; 10 pages
doi:10.1115/DETC2011-47071
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME

abstract

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Copyright © 2011 by ASME

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