A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport.
Saved in:
| Authors: | , , |
|---|---|
| Format: | artículo original |
| Publication Date: | 2021 |
| Description: | 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. |
| Country: | Kérwá |
| Institution: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Language: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/87596 |
| Online Access: | https://academic.oup.com/imajna/article-abstract/41/1/381/5771306?redirectedFrom=fulltext https://hdl.handle.net/10669/87596 |
| Keyword: | Nonlinear transport Brinkman–Darcy coupling Vorticity-based formulation Fixed-point theory Mixed finite elements Error Analysis MATEMÁTICAS |