High order compact finite difference methods for non-Fickian flows in porous media

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)95-111
Journal / PublicationComputers and Mathematics with Applications
Online published22 Feb 2023
Publication statusPublished - 15 Apr 2023


In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in one-dimensional and two-dimensional cases. Stability analyses of the constructed schemes are derived rigorously. We also obtain the optimal second-order convergence in temporal increment and the fourth-order convergence in spatial direction for both velocity and pressure. To verify the validity of the CBCFD schemes, we present some experiments to show that the numerical results are in agreement with our theoretical analysis. © 2023 Elsevier Ltd

Research Area(s)

  • Compact block-centered finite difference, Error estimate, High order scheme, Non-Fickian flows, Numerical simulation