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 - <p style="text-align: justify;">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 L<sup>2&nbsp;</sup>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.</p>