Steady filtration problems with seawater intrusion: Variational analysis

Alduncin, Gonzalo; Esquivel-Avila, Jorge A.; Reyes-Avila, Luis

doi:10.1016/s0045-7825(97)00111-4

Cited by 4 publications

(18 citation statements)

References 14 publications

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“…Sharp interface models in the stationary regime have been studied mathematically, see for instance [13] for one phase problems and [3,9,2] for two phase problems.…”

Section: Brief Review Of Some Related Literaturementioning

confidence: 99%

Derivation of Seawater Intrusion Models by Formal Asymptotics

Jazar¹,

Monneau

2014

SIAM J. Appl. Math.

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In this paper, we consider the flow of fresh and saltwater in a saturated porous medium in order to describe the seawater intrusion. Starting from a formulation with constant densities respectively of fresh and saltwater, whose velocities are proportional to the gradient of pressure (Darcy's law), we consider the formal asymptotic limit as the aspect ratio between the thickness and the horizontal length of the porous medium tends to zero. In the limit of the regime defined by the Dupuit-Forchheimer condition, we identify reduced models of Boussinesq type both in the cases of unconfined and confined aquifers. MSC: 35R35, 35B40

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“…Sharp interface models in the stationary regime have been studied mathematically, see for instance [13] for one phase problems and [3,9,2] for two phase problems.…”

Section: Brief Review Of Some Related Literaturementioning

confidence: 99%

Derivation of Seawater Intrusion Models by Formal Asymptotics

Jazar¹,

Monneau

2014

SIAM J. Appl. Math.

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“…From the above results, the physical problem can be extended variationally from A to all of in the following sense, with an inequality structure due to the presence of the velocity seepage constraint (3) 2 [12].…”

Section: The Variational Modelmentioning

confidence: 99%

“…Global variational problem (V) has a solution, and this is unique whenever every molecule of the uid inside the aquifer is connected to the reservoirs (see Reference [12] for details and other qualitative properties).…”

Section: The Variational Modelmentioning

confidence: 99%

“…We next introduce the penalized formulation of variational problem (V), studied in Reference [12], and, on the basis of nonoverlapping domain decomposition techniques, we derive the corresponding macro-hybrid variational formulation.…”

Section: Penalized Variational Formulationsmentioning

confidence: 99%

“…For the variational formulation of this global problem, according to Reference [12], the following geometrical hypotheses are required:…”

Section: Introductionmentioning

confidence: 99%

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Steady filtration problems with seawater intrusion: macro‐hybrid penalized finite element approximations

Alduncin

Esquivel-Avila

Vera-Guzmán

2005

Numerical Methods in Fluids

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SUMMARYMacro-hybrid penalized ÿnite element approximations are studied for steady ÿltration problems with seawater intrusion. On the basis of nonoverlapping domain decompositions with vertical interfaces, sections of coastal aquifers are decomposed into subsystems with simpler geometries and small scales, interconnected via transmission conditions of pressure and ux continuity. Corresponding local penalized formulations are derived from the global penalized variational formulation of the two-free boundary ow problem, with continuity transmission conditions modelled variationally in a dual sense. Then, macrohybrid ÿnite element approximations are derived for the system, deÿned on independent subdomain grids. Parallel relaxation penalty-duality algorithms are proposed from ÿxed-point problem characterizations. Numerical experiments exemplify the macro-hybrid penalized theory, showing a good agreement with previous primal conforming penalized ÿnite element approximations (Comput. Methods Appl. Mech. Engng. 2000; 190:609-624).

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Steady filtration problems with seawater intrusion: Penalized finite element approximations

Alduncin

Esquivel-Avila

2000

Computer Methods in Applied Mechanics and Engineering

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Steady filtration problems with seawater intrusion: Variational analysis

Cited by 4 publications

References 14 publications

Derivation of Seawater Intrusion Models by Formal Asymptotics

Derivation of Seawater Intrusion Models by Formal Asymptotics

Steady filtration problems with seawater intrusion: macro‐hybrid penalized finite element approximations

Steady filtration problems with seawater intrusion: Penalized finite element approximations

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