scholarly journals Multiscale dimension reduction for flow and transport problems in thin domain with reactive boundaries

2021 ◽  
pp. 110512
Author(s):  
Maria Vasilyeva ◽  
Valentin Alekseev ◽  
Eric T. Chung ◽  
Yalchin Efendiev
Keyword(s):  
Dimension Reduction ◽  
Thin Domain ◽  
Flow And Transport ◽  
Transport Problems

scholarly journals DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

2021 ◽  
Vol 81 ◽  
pp. 423-443 ◽  
Author(s):  
Timo Koch ◽  
Dennis Gläser ◽  
Kilian Weishaupt ◽  
Sina Ackermann ◽  
Martin Beck ◽  
...  
Keyword(s):  
Porous Media ◽  
Open Source ◽  
Model Coupling ◽  
Flow And Transport ◽  
Transport Problems

scholarly journals Dimension reduction and homogenization of random degenerate operators. Part I

2012 ◽  
Vol 15 ◽  
pp. 1-22
Author(s):  
Abdelaziz Aït Moussa ◽  
Loubna Zlaïji
Keyword(s):  
Boundary Conditions ◽  
Dimension Reduction ◽  
Random Function ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Limit Problem ◽  
Thin Domain ◽  
Small Thickness ◽  
Degenerate Equations ◽  
Degenerate Operators

AbstractOur aim in this paper is to identify the limit behavior of the solutions of random degenerate equations of the form −div Aε(x′,∇Uε)+ρεω(x′)Uε=F with mixed boundary conditions on Ωε whenever ε→0, where Ωε is an N-dimensional thin domain with a small thickness h(ε), ρεω(x′)=ρω(x′/ε), where ρω is the realization of a random function ρ(ω) , and Aε(x′,ξ)=a(Tx′ /εω,ξ) , the map a(ω,ξ) being measurable in ω and satisfying degenerated structure conditions with weight ρ in ξ. As usual in dimension reduction problems, we focus on the rescaled equations and we prove that under the condition h(ε)/ε→0 , the sequence of solutions of them converges to a limit u0, where u0 is the solution of an (N−1) -dimensional limit problem with homogenized and auxiliary equations.

PARABOLIC AND DEGENERATE PARABOLIC MODELS FOR PRESSURE-DRIVEN TRANSPORT PROBLEMS

2010 ◽  
Vol 20 (04) ◽  
pp. 543-566 ◽  
Author(s):  
CATHERINE CHOQUET
Keyword(s):  
Existence Result ◽  
Parabolic Type ◽  
Sedimentary Basins ◽  
Coupled System ◽  
Hyperbolic Type ◽  
Flow And Transport ◽  
Partially Saturated ◽  
Saturated Media ◽  
Degenerate Parabolic ◽  
Transport Problems

We consider two models of flow and transport in porous media, the first one for consolidational flow in compressible sedimentary basins, the second one for flow in partially saturated media. Despite the differences in these physical settings, they lead to quite similar mathematical models with a strong pressure coupling. The first model is a coupled system of pde's of parabolic type. The second one involves a coupled system of pdes of degenerate parabolic–hyperbolic type. We state an existence result of weak solutions for both models.

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