Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem
We investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting of multiple species. An approach inspired by augmented Lagrangian methods allows us to construct a symmetric positive defini...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Oxford University Press
2021
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| _version_ | 1826309728928530432 |
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| author | Van-Brunt, A Farrell, PE Monroe, CW |
| author_facet | Van-Brunt, A Farrell, PE Monroe, CW |
| author_sort | Van-Brunt, A |
| collection | OXFORD |
| description | We investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting of multiple species. An approach inspired by augmented Lagrangian methods allows us to construct a symmetric positive definite augmented Onsager transport matrix, which in turn leads to an effective numerical algorithm. We prove inf-sup conditions for the continuous and discrete linearized systems and obtain error estimates for a phase consisting of an arbitrary number of species. The discretization preserves the thermodynamically fundamental Gibbs–Duhem equation to machine precision independent of mesh size. The results are illustrated with numerical examples, including an application to modelling the diffusion of oxygen, carbon dioxide, water vapour and nitrogen in the lungs. |
| first_indexed | 2024-03-07T07:40:03Z |
| format | Journal article |
| id | oxford-uuid:daf378f6-18b3-4988-a09c-d0d353fb1046 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:40:03Z |
| publishDate | 2021 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:daf378f6-18b3-4988-a09c-d0d353fb10462023-04-04T12:07:51ZAugmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:daf378f6-18b3-4988-a09c-d0d353fb1046EnglishSymplectic ElementsOxford University Press2021Van-Brunt, AFarrell, PEMonroe, CWWe investigate structure-preserving finite element discretizations of the steady-state Stefan–Maxwell diffusion problem, which governs mass transport within a phase consisting of multiple species. An approach inspired by augmented Lagrangian methods allows us to construct a symmetric positive definite augmented Onsager transport matrix, which in turn leads to an effective numerical algorithm. We prove inf-sup conditions for the continuous and discrete linearized systems and obtain error estimates for a phase consisting of an arbitrary number of species. The discretization preserves the thermodynamically fundamental Gibbs–Duhem equation to machine precision independent of mesh size. The results are illustrated with numerical examples, including an application to modelling the diffusion of oxygen, carbon dioxide, water vapour and nitrogen in the lungs. |
| spellingShingle | Van-Brunt, A Farrell, PE Monroe, CW Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem |
| title | Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem |
| title_full | Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem |
| title_fullStr | Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem |
| title_full_unstemmed | Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem |
| title_short | Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem |
| title_sort | augmented saddle point formulation of the steady state stefan maxwell diffusion problem |
| work_keys_str_mv | AT vanbrunta augmentedsaddlepointformulationofthesteadystatestefanmaxwelldiffusionproblem AT farrellpe augmentedsaddlepointformulationofthesteadystatestefanmaxwelldiffusionproblem AT monroecw augmentedsaddlepointformulationofthesteadystatestefanmaxwelldiffusionproblem |