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Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media

Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media
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Year:    2018

Author:    Xiaoli Li, Hongxing Rui

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1701-m2016-0628

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 492–516

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

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

Author Details

Xiaoli Li

Hongxing Rui

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