Numerical Solution and Analysis of Three-Dimensional Transient Darcy Flow

Shahab U. Ansari*, Masroor Hussain, Ahmar Rashid, Suleman Mazhar, S. M. Ahmad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper presents a detailed analysis of a numerical solution of three-dimensional transient Darcy flow. The numerical solution of the governing parabolic partial differential equations is obtained by using stabilized mixed Galerkin method and backward Euler method for the discretization of space and time, respectively. The resulting well-posed system of algebraic equations is subsequently solved using conjugate gradient method. The proposed model is validated against Mongan’s analytical model for underground water flow using a set of hexahedral and tetrahedral meshes. The model is used to analyze the transient behavior by simulating the Darcy flow through homogeneous and heterogeneous as well as isotropic and anisotropic media. For large meshes, a parallel algorithm of the transient Darcy flow is also developed for shared memory architecture using OpenMP library. For structured meshes, a speedup of over 22 is obtained on dual AMD Opteron processors. The proposed numerical method for transient Darcy flow offers stability, ease of implementation in higher dimensions and parallel solution for large and complex geometry using standard finite element spaces.

Original languageEnglish
Pages (from-to)289-305
Number of pages17
JournalTransport in Porous Media
Issue number2
StatePublished - 1 Jun 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media B.V., part of Springer Nature.


  • Darcy flow
  • Galerkin method
  • OpenMP
  • Stabilized mixed method
  • Transient flow

ASJC Scopus subject areas

  • Catalysis
  • General Chemical Engineering


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