A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport.
Fecha
2021-01
Tipo
artículo original
Autores
Álvarez Guadamuz, Mario Andrés
Gatica Pérez, Gabriel Nibaldo
Ruiz Baier, Ricardo
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Resumen
This paper is devoted to the mathematical and numerical analysis of a model describing the interfacial
flow-transport interaction in a porous-fluidic domain. The medium consists of a highly permeable
material, where the flow of an incompressible viscous fluid is governed by Brinkman equations (written in
terms of vorticity, velocity and pressure), and a porous medium where Darcy’s law describes fluid motion
using filtration velocity and pressure. Gravity and the local fluctuations of a scalar field (representing
for instance, the solids volume fraction or the concentration of a contaminant) are the main drivers of
the fluid patterns on the whole domain, and the Brinkman-Darcy equations are coupled to a nonlinear
transport equation accounting for mass balance of the scalar concentration. We introduce a mixedprimal
variational formulation of the problem and establish existence and uniqueness of solution using
fixed-point arguments and small-data assumptions. A family of Galerkin discretizations that produce
divergence-free discrete velocities is also presented and analysed using similar tools to those employed in
the continuous problem. Convergence of the resulting mixed-primal finite element method is proven, and
some numerical examples confirming the theoretical error bounds and illustrating the performance of the
proposed discrete scheme are reported.
Descripción
Palabras clave
Nonlinear transport, Brinkman–Darcy coupling, Vorticity-based formulation, Fixed-point theory, Mixed finite elements, Error Analysis, MATEMÁTICAS