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

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.