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# Tesis de Pregrado de Sebastián Domínguez

CarreraIngeniería Civil Matemática, Universidad de Concepción
Año de Ingreso2007
Año de Egreso2015
Título de la TesisUna Formulación Primal-Mixta para el Acoplamiento Fuerte de Fluidos Quasi-Newtonianos con Medios Porosos

#### Resumen de la Tesis:

In this thesis we analyze a primal-mixed finite element method for the coupling of quasi-Newtonian fluids with porous media in 2D and 3D. The flows are governed by a class of nonlinear Stokes and linear Darcy equations, respectively, and the transmission conditions on the interface between the fluid and the porous medium are given by mass conservation, balance of normal forces and the Beavers-Joseph-Saffman law. We apply a primal formulation in the Stokes domain and a mixed formulation in the Darcy formulation. The strong coupling concept means that the conservation of mass across the interface is introduced as an essential condition in the space where the velocity unknowns live. In this way, under some assumptions on the nonlinear kinematic viscosity, a generalization of the Babuska-Brezzi theory is utilized to show the well posedness of our primal-mixed formulation. Then, we introduce a Galerkin scheme in which the discrete conservation of mass is imposed approximately through an orthogonal projector. The unique solvability of this discrete system and its Strang-type error estimate follow from the generalized Babuska-Brezzi theory as well. In particular, the feasible finite element subspaces include Bernadi-Raugel elements for the Stokes flow, and either the Raviart-Thomas elements of lowest order or the Brezzi-Douglas-Marini elements of first order for the Darcy flow, which yield non-conforming and conforming Galerkin schemes, respectively. In turn, piecewise constant functions are employed to approximate in both cases the global pressure field in the Stokes and Darcy domain. Finally, several numerical results illustrating the good performance of both discrete methods and confirming the theoretical rates of convergence, are provided.

Director(es) de Tesis Gabriel N. Gatica
Fecha de Aprobación Proyecto de Tesis2013, Abril 04
Fecha de Defensa de Tesis2015, Enero 05
Seguimiento Profesional
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#### Publicaciones Originadas de la Tesis (ISI)

Sebastian DOMINGUEZ, Gabriel N. GATICA, Antonio MARQUEZ, Salim MEDDAHI: A primal-mixed formulation for the strong coupling of quasi-Newtonian fluids with porous media. Advances in Computational Mathematics, vol. 42, 3, pp. 675-720, (2016).