Abstract
Two different coupling approaches for isothermal single-phase free flow and isothermal single-fluid-phase porous medium systems are considered: sharp interface and transition region approach. The sharp interface concept implies the Beavers–Joseph–Saffman velocity jump condition together with restrictions that arise due to mass conservation and balance of normal forces across the fluid-porous interface. The transition region model is derived by means of the thermodynamically constrained averaging theory (TCAT). The equations are averaged over the thickness of the transition zone in the direction normal to the free flow and porous medium domains being joined. Coupling conditions are the mass conservation, the momentum balance and a generalization of the Beavers–Joseph condition. Two model formulations are compared and numerical simulation results are presented. For discretization of the coupled problem the finite volume method on staggered grids is used.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beavers, G., Joseph, D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967)
Cimolin, F., Discacciati, M.: Navier-Stokes/Forchheimer models for filtration through porous media. Appl. Numer. Math. 72, 205–224 (2013)
Discacciati, M., Miglio, E., Quarteroni, A.: Mathematical and numerical models for coupling surface and groundwater flows. Appl. Num. Math. 43, 57–74 (2002)
Goyeau, B., Lhuillier, D., Gobin, D., Velarde, M.: Momentum transport at a fluid-porous interface. Int. J. Heat Mass Transf. 46, 4071–4081 (2003)
Gray, W., Miller, C.: Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow. Adv. Water Res. 29, 1745–1765 (2006)
Jackson, A., Rybak, I., Helmig, R., Gray, W., Miller, C.: Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 9. Transition region models. Adv. Water Res. 42, 71–90 (2012)
Layton, W., Schieweck, F., Yotov, I.: Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40, 2195–2218 (2003)
Le Bars, M., Worster, M.: Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification. J. Fluid Mech. 550, 149–173 (2006)
Mosthaf, K., Baber, K., Flemisch, B., Helmig, R., Leijnse, A., Rybak, I., Wohlmuth, B.: A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow. Water Resour. Res. 47, W10,522 (2011)
Saffman, R.: On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50, 93–101 (1971)
Versteeg, H., Malalasekra, W.: An introduction to computational fluid dynamics: The finite volume method. Prentice Hall, NJ (2007)
Acknowledgments
This work was supported by the German Research Foundation (DFG) project RY 126/2-1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Rybak, I. (2014). Coupling Free Flow and Porous Medium Flow Systems Using Sharp Interface and Transition Region Concepts. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_70
Download citation
DOI: https://doi.org/10.1007/978-3-319-05591-6_70
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05590-9
Online ISBN: 978-3-319-05591-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)