Validating numerical solution of transient Darcy flow using the stabilized mixed finite element method

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The natural flows through porous media often exhibit transient behavior. Some of the examples include water movement in aquifers, oil flow in reservoirs and blood passing through arteries walls. For accurate modeling of such flows, the Darcy model is used with an additional time-dependent pressure term. In this paper, validation of the three-dimensional numerical solution of transient Darcy flow using the stabilized mixed finite element method is presented. The proposed numerical solution employs the implicit backward difference method for the discretization of time, whereas, for space discretization, the Galerkin technique is used. The model is validated against analytical models including the Theis equation for pressure drawdown near a pumping well. The proposed solution is tested for different values of the viscosity of the fluid, and the permeability and specific storage of the medium. The error analysis shows that the stabilized mixed Galerkin methods give stable solutions with no oscillations and spurious results. It is also found that the viscosity of the fluid and the permeability of the medium have prominent effects on the transient behavior of Darcy flow.

Original languageEnglish
Pages (from-to)55-65
Number of pages11
JournalSimulation
Volume94
Issue number1
DOIs
StatePublished - 1 Jan 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, © The Author(s) 2017.

Keywords

  • Darcy flow
  • mixed finite element method
  • stabilized mixed method
  • transient flow

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Graphics and Computer-Aided Design

Fingerprint

Dive into the research topics of 'Validating numerical solution of transient Darcy flow using the stabilized mixed finite element method'. Together they form a unique fingerprint.

Cite this