Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem

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...

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Үндсэн зохиолчид: Anaya, V, Mora, D, Reales, C, Ruiz Baier, R
Формат: Journal article
Хэвлэсэн: Wiley 2018
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author Anaya, V
Mora, D
Reales, C
Ruiz Baier, R
author_facet Anaya, V
Mora, D
Reales, C
Ruiz Baier, R
author_sort Anaya, V
collection OXFORD
description 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.
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spelling oxford-uuid:7ec6bfd0-47fb-46b3-8ef4-ec3f1c3df9b32022-03-26T21:12:20ZVorticity‐pressure formulations for the Brinkman‐Darcy coupled problemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7ec6bfd0-47fb-46b3-8ef4-ec3f1c3df9b3Symplectic Elements at OxfordWiley2018Anaya, VMora, DReales, CRuiz Baier, RWe 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.
spellingShingle Anaya, V
Mora, D
Reales, C
Ruiz Baier, R
Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
title Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
title_full Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
title_fullStr Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
title_full_unstemmed Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
title_short Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
title_sort vorticity pressure formulations for the brinkman darcy coupled problem
work_keys_str_mv AT anayav vorticitypressureformulationsforthebrinkmandarcycoupledproblem
AT morad vorticitypressureformulationsforthebrinkmandarcycoupledproblem
AT realesc vorticitypressureformulationsforthebrinkmandarcycoupledproblem
AT ruizbaierr vorticitypressureformulationsforthebrinkmandarcycoupledproblem