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Volume 36, Issue 4
Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media

Xiaoli Li & Hongxing Rui

DOI: 10.4208/jcm.1701-m2016-0628

J. Comp. Math., 36 (2018), pp. 492-516.

Published online: 2018-06

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  • Abstract

In this article, two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment. Stability analysis and second-order error estimates in spatial mesh size for both pressure and velocity in discrete L2 norms are established on non-uniform rectangular grid. Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.

  • Keywords

Block-centered finite difference, Parabolic integro-differential equation, Non-uniform, Error estimates, Numerical analysis.

  • AMS Subject Headings

65N06, 65N12, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiaolisdu@163.com (Xiaoli Li)

hxrui@sdu.edu.cn (Hongxing Rui)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-492, author = {Li , Xiaoli and Rui , Hongxing}, title = {Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {492--516}, abstract = {

In this article, two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment. Stability analysis and second-order error estimates in spatial mesh size for both pressure and velocity in discrete L2 norms are established on non-uniform rectangular grid. Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1701-m2016-0628}, url = {http://global-sci.org/intro/article_detail/jcm/12302.html} }
TY - JOUR T1 - Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media AU - Li , Xiaoli AU - Rui , Hongxing JO - Journal of Computational Mathematics VL - 4 SP - 492 EP - 516 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1701-m2016-0628 UR - https://global-sci.org/intro/article_detail/jcm/12302.html KW - Block-centered finite difference, Parabolic integro-differential equation, Non-uniform, Error estimates, Numerical analysis. AB -

In this article, two block-centered finite difference schemes are introduced and analyzed to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. One scheme is Euler backward scheme with first order accuracy in time increment while the other is Crank-Nicolson scheme with second order accuracy in time increment. Stability analysis and second-order error estimates in spatial mesh size for both pressure and velocity in discrete L2 norms are established on non-uniform rectangular grid. Numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis.

Li , Xiaoli and Rui , Hongxing. (2018). Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media. Journal of Computational Mathematics. 36 (4). 492-516. doi:10.4208/jcm.1701-m2016-0628
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