Transport in Porous Media

, Volume 92, Issue 1, pp 101–118 | Cite as

Analysis of Momentum Transfer in a Lid-Driven Cavity Containing a Brinkman–Forchheimer Medium

  • Duoxing YangEmail author
  • Ziqiu Xue
  • Simon A. Mathias


The CE/SE (the space-time conservation element and solution element method) scheme with the second-order accuracy has been proposed. And the pretreatment method has been introduced to convert the parabolic equations to the hyperbolic equations, which are accurately solved by the CE/SE method. The lid-driven rectangular cavity containing a porous Brinkman–Forchheimer medium is studied in this numerical investigation. The Brinkman–Forchheimer equation is used such that both the inertial and viscous effects are incorporated. The governing equations are solved by the improved CE/SE approach. The characteristics of the flow are analyzed with emphasis on the influence of the Darcy number and the cavity depth. It is found that the porous medium effect decreases both the strength and the number of eddies, especially for deep cavities.


Lid-driven cavity flow Porous medium CE/SE method CO2 storage Forchheimer 

List of symbols


Dimensionless volume-averaged velocity vector [–]


Dimensionless pressure [–]

α = μe/μ

Viscosity ratio [–]


Shear viscosity of the fluid [ML−1T−1]


Effective viscosity [ML−1T−1]

Re = LU/μ

Reynolds number [–]


Porosity [–]


Darcy number [–]


Dimensionless time [–]


Characteristic length [L]


Characteristic velocity [LT−1]


Depth ratio [–]


Forchheimer parameter (Geometric function) [L−1]


Permeability [L2]


Dimensionless horizontal velocity [–]


Dimensionless vertical velocity [–]


Dimensionless virtual time [–]


Artificial compressibility coefficient [–]


Dimensionless density [–]

(j, k, n)

Space-time mesh points


Vectors of primary variable


Flux in x-direction


Flux in y-direction


Source term vector


Components of the source term vector

S (V)

Boundary of an arbitrary space-time region


Space-time region

Area of a surface element


Outward unit normal of a surface element

P′(j, k, n)

Spatial point


Space-time flux vector


Components of vector Q


Components of vector E


Components of vector F


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of Crustal Dynamics, CEABeijingPeople’s Republic of China
  2. 2.Research Institute of Innovative Technology for the Earth (RITE)KyotoJapan
  3. 3.Department of Earth SciencesDurham UniversityDurhamUK

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