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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/3884

Title: Modelling Complex Flows in Porous Media by Means of Upscaling Procedures
Authors: Fasano, Antonio
Farina, Angiolo
Keywords: Flow in Porous Media
Free Boundary Problems
Fluid Dynamics
Issue Date: 2010
Publisher: EUT Edizioni Università di Trieste
Citation: Antonio Fasano, Angiolo Farina, "Modelling Complex Flows in Porous Media by Means of Upscaling Procedures", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 42 (2010), pp. 65-102.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 (2010)
Abstract: We review a series of problems arising in the field of flows through porous media and that are highly nontrivial either because of the presence of mass exchange between the fluid and the porous matrix (or other concurrent phenomena of physical or chemical nature), or because of a particularly complex structure of the medium. In all these cases there is a small parameter $\varepsilon $, representing the ratio between the microscopic and the macroscopic space scale. Our attention is focussed on a modelling technique (upscaling) which start from the governing equations written at the pore scale, introduces an expansion in power series of $\varepsilon $of all the relevant quantities and eventually leads to the formulation of the macroscopic governing equations at the various orders in $\varepsilon $ by a matching procedure, followed by suitable averaging. Two problems will be analyzed with some detail: soil erosion and the dynamics of water ultrafiltration devices. Moreover other problems will be occasionally discussed and open questions will be proposed.
URI: http://hdl.handle.net/10077/3884
ISSN: 0049-4704
MS Classification 2000: 76S05
76-02
35R35
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.42 (2010)

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