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UID:7162@test.i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210831T000000
DTEND;TZID=Europe/Paris:20210831T000000
DTSTAMP:20210830T073800Z
URL:https://test.i2m.univ-amu.fr/events/thematic-day-of-applied-analysis-p
orous-media-interface-and-upscaling-problems-in-porous-fluid-flows/
SUMMARY:Thematic day of Applied Analysis: Porous media: interface and upsca
ling problems in porous-fluid flows - Workshop
DESCRIPTION:Thematic day of Applied Analysis: Porous media: interface and u
pscaling problems in porous-fluid flows\nJournée thématique d'Analyse Ap
pliquée: Fluide-poreux : Problèmes d'interface et d'upscaling dans les
écoulements fluide-poreux\n\n\nLocal project leaders:\nPhilippe Angot
(Aix-Marseille Université)\nThomas Ourmières-Bonafos (Aix-Marseille Univ
ersité)contact: fluide-poreux@sciencesconf.org\n\n\n\n\n\n \;\n\n\n\n
\nParticipants\n\n[su_spacer size="30"]\n\nElissa Eggenweiler (University
of Stuttgart)\nGeneralized coupling conditions for multidimensional flows
in Stokes/Darcy systems\nExisting coupling concepts for the Stokes/Darcy
problem are limited for one-dimensional flows (parallel or perpendicular
to the interface)\, are not validated for multidimensional flows (arbitra
ry to the porous bed)\, or contain unknown model parameters\, which need
to be determined.\nIn this talk\, we present generalized interface conditi
ons valid for multidimensional flows in Stokes/Darcy systems. These condi
tions are derived rigorously using periodic homogenization and boundary l
ayer theory\, and all effective parameters can be computed based on the
pore geometry. We prove the well-posedness of the coupled Stokes/Darcy pr
oblem with the generalized conditions and validate the macroscale model u
sing pore-scale resolved simulations.\n[su_spacer size="10"]\nMarco Disca
cciati (Loughborough University)\nDomain decomposition methods for the Sto
kes-Darcy problem\nThe Stokes-Darcy problem has received a growing attenti
on by the mathematical community over the last decade not only due to its
many possible applications but also to its mathematical nature. Indeed\, i
t is a good example of a multi-physics problem where two different boundar
y value problems are coupled into a global heterogeneous one.\nThe multi-p
hysics nature of the problem makes it suitable to domain decomposition tec
hniques which permit to recover the solution of the coupled problem by sol
ving the fluid and the porous-medium subproblems separately in an iterativ
e way.\nThis talk will provide an overview of different non-overlapping an
d overlapping approaches for the Stokes-Darcy problem considering the conv
ergence and robustness of these methods as well as related modelling aspec
ts. Some numerical examples will show the effectiveness of the methods for
problems arising in practical applications.\n[su_spacer size="10"]\nIryna
Rybak (University of Stuttgart)\nHybrid-dimensional Stokes-Darcy model f
or fractured porous media\nHybrid-dimensional models for flow and transpor
t processes in fractured porous media are effective approximations of ful
l-dimensional models. Traditionally applied mixed-dimensional Darcy-Darcy
models fail to adequately describe flow and transport through fractures
which act as conduits and separate rock matrices with significantly diffe
rent permeability. We propose a hybrid-dimensional Stokes-Darcy model for
flows in fractured porous media. The fractures can store and transport
fluid and they are modeled as lower-dimensional entities in the surroundi
ng porous medium. The well-posedness of the proposed coupled model is pro
ved under a mild restriction on the fracture aperture. The developed mode
l is validated against the full-dimensional model and compared to the hyb
rid-dimensional Darcy-Darcy model.\n[su_spacer size="10"]\nCatherine Choqu
et (Université de la Rochelle)\nCoupling of models that should hold at di
fferent scales\nContamination of soil and groundwater is a major concern t
hat affects all populated areas. It is all the more important that groundw
ater pollution can be rapid and its remediation very long. A challenge is
therefore to develop models to monitor the vulnerability of aquifers in a
context of very heterogeneous time scales. In this talk\, we propose nonli
near moving boundary problems describing the exchanges between the overlan
d and the underground water\, saltwater intrusion in coastal areas\, agric
ultural\, industrial\, or sewage pollution. Let's use the example of th
e recharge of aquifers by overland water. We aim at keeping track of (at
least) two types of flow: the first is essentially vertical and it is dom
inant on a small time scale (Richards flow) and the second\, that is essen
tially horizontal\, corresponds to a large time scale (Dupuit flow). Such
a model cannot be justified by arguments of classical asymptotic analysis.
Indeed\, the scales allowing to justify a Richards model from Darcy's are
very different from those allowing to obtain a Dupuit model from Darcy's.
We thus propose another approach. The asymptotic analysis is not used fo
r deriving an effective model for a given reference time\; rather\, we wan
t that the new model and the exact model are associated with the same effe
ctive problem for any time scale. The process allows to define some virtua
l interface (that does not necessarily coincide with the water table) sepa
rating an essentially vertical flow from an essentially horizontal one. In
this presentation\, the asymptotic analysis approach\, the definition of
the interface over time\, numerical illustrations and some mathematical di
fficulties related to the structure of the new model will be discussed...\
n[su_spacer size="20"]\nExternal dedicated website\n\n\n\n\n\n \n\nTRUSTE
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CATEGORIES:Manifestation scientifique,Workshop
LOCATION:CIRM\, Luminy\, 163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=CIRM\, Luminy:geo:0,0
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DTSTART:20210328T030000
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