By V. Girault, G. Kanschat, B. Rivière (auth.), José A. Ferreira, Sílvia Barbeiro, Gonçalo Pena, Mary F. Wheeler (eds.)
This quantity offers a range of survey and study articles in keeping with invited lectures and contributed talks awarded on the Workshop on Fluid Dynamics in Porous Media that was once held in Coimbra, Portugal, in September 12-14, 2011. The contributions are dedicated to mathematical modeling, numerical simulation and their purposes, offering the readers a cutting-edge evaluation at the most up-to-date findings and new demanding situations at the subject. The e-book comprises study paintings of globally famous leaders of their respective fields and provides advances in either idea and purposes, making it attractive to an unlimited variety of viewers, particularly mathematicians, engineers and physicists.
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Extra resources for Modelling and Simulation in Fluid Dynamics in Porous Media
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J j j b ρ jv j b j ρ jv j j + ρ jv j f j j + b fj ¨ + ρj ρj fj j + fj j 1 ρj ε 2j = fj j (12) b The volume averages of the time derivative and gradient of a property f of the j-phase are given, respectively, by [10, 18, 20] ≠ ∂ fj ∂t ∑ = b = ∂ fj ∂t − b 1 Vb ∂ (ε j f j j ) ∂t f j vA j · n j dA Aj − 1 Vb f j vA j · n j dA, (13) Aj and ∇fj b = ∇ fj b + 1 Vb f j n j dA = ∇ j Aj Ä ä 1 εj fj j + Vb f j n j dA. (14) Aj Although frequently used in the literature, their derivations involve some assumptions which are not rigorously correct such as the consideration of the volumetric and area averages to be the same .