论文标题
稳态Stefan-Maxwell扩散问题的增强马鞍点配方
Augmented saddle point formulation of the steady-state Stefan--Maxwell diffusion problem
论文作者
论文摘要
我们研究了稳态Stefan-Maxwell扩散问题的结构提供有限元离散化，该问题控制着由多种物种组成的相扩散。一种受增强拉格朗日方法启发的方法使我们能够构建一种对称的确定的增强式Onsager运输矩阵，进而导致有效的数值算法。我们证明了连续和离散线性化系统的INF-SUP条件，并获得由任意数量的物种组成的相位的错误估计。离散化保留了热力学基本的Gibbs-与网格尺寸无关的机器精度方程。结果用数值示例说明了结果，包括用于建模氧气中氧，二氧化碳，水蒸气和氮的扩散。
We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion 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.
