Augmented saddle-point formulation of the steady-state Stefan–Maxwell diffusion problem. (6th October 2021)

• Record Type: Journal Article
• Authors: Van-Brunt, Alexander; Farrell, Patrick E; Monroe, Charles W
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 4(2022)
• Page Start: 3272
• Page End: 3305
• Publication Date: 2021-10-06
• Subjects: Stefan–Maxwell equations -- multicomponent diffusion -- augmented saddle-point formulation; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab067
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: 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.