Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem

Journal article

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.

Authors: Van-Brunt, A; Farrell, PE; Monroe, CW

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Oxford University Press
• Journal: IMA Journal of Numerical Analysis
• Volume: 42
• Issue: 4
• Pages: 3272-3305
• Publication date: 2021-10-06
• Acceptance date: 2021-08-01
• DOI: 10.1093/imanum/drab067
• EISSN: 1464-3642
• ISSN: 0272-4979
• Language: English
• Keywords: FFR; augmented saddle-point formulation; Stefan–Maxwell equations; multicomponent diffusion