2020/06/05 by Alexander Van–Brunt, Patrick E. Farrell, Van-Brunt, Alexander +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Nuclear reactor physics and engineering #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2006.03321
openalex publication_date 2020/06/05 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We investigate structure-preserving finite element discretizations of the\nsteady-state Stefan--Maxwell diffusion problem which governs diffusion within a\nphase consisting of multiple species. An approach inspired by augmented\nLagrangian methods allows us to construct a symmetric positive definite\naugmented Onsager transport matrix, which in turn leads to an effective\nnumerical algorithm. We prove inf-sup conditions for the continuous and\ndiscrete linearized systems and obtain error estimates for a phase consisting\nof an arbitrary number of species. The discretization preserves the\nthermodynamically fundamental Gibbs--Duhem equation to machine precision\nindependent of mesh size. The results are illustrated with numerical examples,\nincluding an application to modelling the diffusion of oxygen, carbon dioxide,\nwater vapour and nitrogen in the lungs.\n