Open AccessA model for incompressible fluids using finite element methods for the Brinkman problem
Author(s) -
A Altamirano-Fernández,
Enith A. Gómez-Hernández,
E. Duque-Marín,
Arturo Vasquez
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1702/1/012001
Subject(s) - mathematics , finite element method , discretization , piecewise , incompressible flow , vorticity , fluid dynamics , mathematical analysis , compressibility , partial differential equation , uniqueness , boundary value problem , flow (mathematics) , mechanics , physics , geometry , vortex , thermodynamics
The partial differential equations for fluid flow dynamics based on the Brinkman equations, written in terms of velocity-vorticity and pressure in three dimensions, are essential for predicting climate, ocean currents, water flow in a pipe, the study of blood flow and any phenomenon involving incompressible fluids through porous media; having a significant impact in areas such as oceanographic engineering and biomedical sciences. This paper aims to study the Brinkman equations with homogeneous Dirichlet boundary are studied, the existence and uniqueness of solution at a continuous level through equivalence of problems is presented. It is discretized to approximate the solution using Nédélec finite elements and piecewise continuous polynomials to approximate vorticity and pressure. The velocity field is recovered, obtaining its a priori error estimation and order of convergence. As a result, ensuring a single prediction of the flow behavior of an incompressible fluid through porous media. Finally, a numerical example in 2D with the standard L 2 is presented, confirming the theoretical analysis.