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dc.creatorÁlvarez Guadamuz, Mario Andrés
dc.creatorGatica Pérez, Gabriel Nibaldo
dc.creatorRuiz Baier, Ricardo
dc.date.accessioned2022-11-10T19:51:38Z
dc.date.available2022-11-10T19:51:38Z
dc.date.issued2016
dc.identifier.citationhttps://www.sciencedirect.com/science/article/abs/pii/S0045782516302092?via%3Dihubes_ES
dc.identifier.issn1880-3989
dc.identifier.issn0388-1350
dc.identifier.urihttps://hdl.handle.net/10669/87673
dc.description.abstractWe propose and analyze a fully-mixed finite element method to numerically approximate the flow patterns of a viscous fluid within a highly permeable medium (an array of low concentration fixed particles), described by Brinkman equations, and its interaction with non-viscous flow within classical porous media governed by Darcy’s law. The system is formulated in terms of velocity and pressure in the porous medium, together with vorticity, velocity and pressure of the viscous fluid. In addition, and for sake of the analysis, the tangential component of the vorticity is supposed to vanish on the whole boundary of the Brinkman domain, whereas null normal components of both velocities are assumed on the respective boundaries, except on the interface where suitable transmission conditions are considered. In this way, the derivation of the corresponding mixed variational formulation leads to a Lagrange multiplier enforcing the pressure continuity across the interface, whereas mass balance results from essential boundary conditions on each domain. As a consequence, a typical saddle-point operator equation is obtained, and hence the classical Babuˇska–Brezzi theory is applied to establish the well-posedness of the continuous and discrete schemes. In particular, we remark that the continuous and discrete inf–sup conditions of the main bilinear form are proved by using suitably chosen injective operators to get lower bounds of the corresponding suprema, which constitutes a previously known technique, recently denominated T -coercivity. In turn, and consistently with the above, the stability of the Galerkin scheme requires that the curl of the finite element subspace approximating the vorticity be contained in the space where the discrete velocity of the fluid lives, which yields Raviart–Thomas and Nédélec finite element subspaces as feasible choices. Then we show that the aforementioned constraint can be avoided by augmenting the mixed formulation with a residual arising from the Brinkman momentum equation. Finally, several We propose and analyze a fully-mixed finite element method to numerically approximate the flow patterns of a viscous fluid within a highly permeable medium (an array of low concentration fixed particles), described by Brinkman equations, and its interaction with non-viscous flow within classical porous media governed by Darcy’s law. The system is formulated in terms of velocity and pressure in the porous medium, together with vorticity, velocity and pressure of the viscous fluid. In addition, and for sake of the analysis, the tangential component of the vorticity is supposed to vanish on the whole boundary of the Brinkman domain, whereas null normal components of both velocities are assumed on the respective boundaries, except on the interface where suitable transmission conditions are considered. In this way, the derivation of the corresponding mixed variational formulation leads to a Lagrange multiplier enforcing the pressure continuity across the interface, whereas mass balance results from essential boundary conditions on each domain. As a consequence, a typical saddle-point operator equation is obtained, and hence the classical Babuˇska–Brezzi theory is applied to establish the well-posedness of the continuous and discrete schemes. In particular, we remark that the continuous and discrete inf–sup conditions of the main bilinear form are proved by using suitably chosen injective operators to get lower bounds of the corresponding suprema, which constitutes a previously known technique, recently denominated T -coercivity. In turn, and consistently with the above, the stability of the Galerkin scheme requires that the curl of the finite element subspace approximating the vorticity be contained in the space where the discrete velocity of the fluid lives, which yields Raviart–Thomas and Nédélec finite element subspaces as feasible choices. Then we show that the aforementioned constraint can be avoided by augmenting the mixed formulation with a residual arising from the Brinkman momentum equation. Finally, several numerical examples illustrating the satisfactory performance of the methods and confirming the theoretical rates of convergence are reported.es_ES
dc.description.sponsorshipComisión Nacional de Investigación Científica y Tecnológica/[ACT1118]/CONICYT/Chilees_ES
dc.description.sponsorshipMinisterio de Educación/[]//Chilees_ES
dc.description.sponsorshipCentro de Investigación en Ingeniería Matemática/[CI2MA]//Chilees_ES
dc.language.isoenges_ES
dc.sourceComputer Methods in Applied Mechanics and Engineering, Vol. 307, pp. 68-95es_ES
dc.subjectBrinkman equationes_ES
dc.subjectDarcy equationes_ES
dc.subjectVorticity-based formulationes_ES
dc.subjectMixed finite elementses_ES
dc.subjectError analysises_ES
dc.subjectViscous and non-viscous flowses_ES
dc.titleAnalysis of a vorticity–based fully–mixed formulation for 3D Brinkman–Darcy problem.es_ES
dc.typeartículo originales_ES
dc.identifier.doi10.1016/j.cma.2016.04.017
dc.description.procedenceUCR::Sedes Regionales::Sede de Occidentees_ES
dc.description.procedenceUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemáticaes_ES


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