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A Stokes-Brinkman model of the fluid flow in a periodic cell with a porous body using the boundary element method

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journal contribution
posted on 04.01.2018, 17:07 by R.F. Mardanov, S.K. Zaripov, V.F. Sharafutdinov, Sarah DunnettSarah Dunnett
The problem of viscous incompressible flow in a periodic cell with a porous body is solved. The Stokes flow model is adopted to describe the flow outside the body and the Brinkman equation is applied to find the filtration velocity field inside the porous domain. The conditions on the boundary between the free fluid and the porous medium for the porous body of arbitrary shape are obtained. The boundary value problem for the joint solution of the biharmonic and Brinkman equations for the stream functions outside and inside the porous body are then solved using a boundary element method. Good agreement of the numerical and analytical models for the Kuwabara circular cell model is shown for the fluid flow through a porous circular cylinder. The fluid flow past a circular, square, triangular cylinders and a circular body of uneven surface (an idealized model of a viral capsid) in a rectangular periodic cell are calculated. Comparison of the results obtained with the numerical solution from a CFD ANSYS/FLUENT model shows good accuracy of the developed mathematical model.


The work was performed in the frameworks of the Russian Government Program of Competitive Growth at Kazan Federal University and supported by the Russian Foundation for Basic Research (Grants no. 15-01-06135, 16-51-10024).



  • Aeronautical, Automotive, Chemical and Materials Engineering


  • Aeronautical and Automotive Engineering

Published in

Engineering Analysis with Boundary Elements






MARDANOV, R.F. ... et al, 2017. A Stokes-Brinkman model of the fluid flow in a periodic cell with a porous body using the boundary element method. Engineering Analysis with Boundary Elements, 88, pp. 54–63.


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This paper was accepted for publication in the journal Engineering Analysis with Boundary Elements and the definitive published version is available at