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...
| Main Authors: | , , , |
|---|---|
| פורמט: | Journal article |
| יצא לאור: |
Wiley
2018
|
| _version_ | 1826281382700122112 |
|---|---|
| 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. |
| first_indexed | 2024-03-07T00:27:59Z |
| format | Journal article |
| id | oxford-uuid:7ec6bfd0-47fb-46b3-8ef4-ec3f1c3df9b3 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:27:59Z |
| publishDate | 2018 |
| publisher | Wiley |
| record_format | dspace |
| 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 |