PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 10 | 1275-1283
Tytuł artykułu

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1275-1283
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
autor
  • School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, QLD., 4001, Australia
autor
  • School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, QLD., 4001, Australia
Bibliografia
  • [1] R. Metzler, J. Klafter, Phys. Rep. 339, (2000)
  • [2] Y. Zhang, D. A. Benson, D. M. Reeves, Adv. Water Resour. 32, (2009)
  • [3] I. Podlubny, Fractional Differential Equations (Academic Press, 1999)
  • [4] M. M. Meerschaert, C. Tadjeran, Appl. Numer. Math. 56, (2006)
  • [5] K. Oldham, J. Spanier, The fractional calculus: theory and applications of differentiation and integration to arbitrary order (Academic Press, 1974)
  • [6] Y. Lin, C. Xu, J. Comput. Phys. 225, 1533 (2007) http://dx.doi.org/10.1016/j.jcp.2007.02.001[Crossref]
  • [7] M. M. Meerschaert, C. Tadjeran, J. Comput. Appl. Math. 172, (2004)
  • [8] M. M. Meerschaert, H.-P. Scheffler, C. Tadjeran, J. Comput. Phys. 211, (2006)
  • [9] C. Tadjeran, M. M. Meerschaert, H. P. Scheffler, J. Comput. Phys. 213, (2006)
  • [10] K. Moaddy, I. Hashim, S. Momani, Comput. Math. Appl. 62, 1068 (2011) http://dx.doi.org/10.1016/j.camwa.2011.03.059[Crossref]
  • [11] K. Moaddy, S. Momani, I. Hashim, Comput. Math. Appl. 61, 1209 (2011) http://dx.doi.org/10.1016/j.camwa.2010.12.072[Crossref]
  • [12] S. Momani, A. Rqayiq, D. Baleanu, Int. J. Bifurcat. Chaos 22, 1250079 (2012) http://dx.doi.org/10.1142/S0218127412500794[Crossref]
  • [13] P. Zhuang, F. Liu, V. Anh, I. Turner, SIAM J. Numer. Anal. 47, (2012)
  • [14] H. Sun, W. Chen, Y. Chen, Physica A: Statistical Mechanics and its Applications 388, 4586 (2009) http://dx.doi.org/10.1016/j.physa.2009.07.024[Crossref]
  • [15] S. Shen, F. Liu, J. Chen, I. Turner, V. Anh, Appl. Math. Comput. 218, 10861 (2012) http://dx.doi.org/10.1016/j.amc.2012.04.047[Crossref]
  • [16] H. Sun, W. Chen, C. LI, Y. Chen, Int. J. Bifurcat. Chaos 22, 1250085 (2012) http://dx.doi.org/10.1142/S021812741250085X[Crossref]
  • [17] H. Wang, K. Wang, T. Sircar, J. Comput. Phys. 229, 8095 (2010) http://dx.doi.org/10.1016/j.jcp.2010.07.011[Crossref]
  • [18] K. Wang, H. Wang, Adv. Water Resour. 34, 810 (2011) http://dx.doi.org/10.1016/j.advwatres.2010.11.003[Crossref]
  • [19] H.-K. Pang, H.-W. Sun, J. Comput. Phys. 231, 693 (2012) http://dx.doi.org/10.1016/j.jcp.2011.10.005[Crossref]
  • [20] T. Moroney, Q. Yang, Comput. Math. Appl. 66, 659 (2013) http://dx.doi.org/10.1016/j.camwa.2013.01.048[Crossref]
  • [21] T. Moroney, Q. Yang, J. Comput. Phys. 246, 304 (2013) http://dx.doi.org/10.1016/j.jcp.2013.03.029[Crossref]
  • [22] X. Zhang, J. W. Crawford, L. K. Deeks, M. I. Stutter, A. G. Bengough, I. M. Young, Water Resour. Res. 41, (2005)
  • [23] X. Zhang, M. Lv, J. W. Crawford, I. M. Young, Adv. Water Resour. 30, 1205 (2007) http://dx.doi.org/10.1016/j.advwatres.2006.11.002[Crossref]
  • [24] H. Hejazi, T. Moroney, F. Liu, J. Comput. Appl. Math. 255, 684 (2014) http://dx.doi.org/10.1016/j.cam.2013.06.039[Crossref]
  • [25] S. Kim, M. L. Kavvas, J. Hydro. Eng. 1, (2006)
  • [26] Q. Yang, F. Liu, I. Turner, Appl. Math. Model. 34, (2010)
  • [27] S. Shen, F. Liu, V. Anh, Numer. Algorithms 56, (2011)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0317-y
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.