Vorticity-pressure formulations for the Brinkman-Darcy coupled problem

Verónica Anaya, David Mora, Carlos Reales, Ricardo Ruiz-Baier

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Abstract

We introduce a new variational formulation for the Brinkman-Darcy equations formulated in terms of the scaled Brinkman vorticity and the global pressure. The velocities in each subdomain are fully decoupled through the momentum equations, and can be later recovered from the principal unknowns. A new finite element method is also proposed, consisting in equal-order Nédélec and piecewise continuous elements, for vorticity and pressure, respectively. The error analysis for the scheme is carried out in the natural norms, with bounds independent of the fluid viscosity. An adequate modification of the formulation and analysis permits us to specify the presentation to the case of axisymmetric configurations. We provide a set of numerical examples illustrating the robustness, accuracy, and efficiency of the proposed discretization.

Original languageEnglish
Pages (from-to)528-544
Number of pages17
JournalNumerical Methods for Partial Differential Equations
Volume35
Issue number2
DOIs
Publication statusPublished - 1 Mar 2019
Externally publishedYes

Keywords

  • Brinkman-Darcy coupling
  • error analysis
  • finite element methods
  • interface problems
  • vorticity-pressure formulation

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