We present a broad family of high-order finite element algorithms for simulating the flow of electroneutral electrolytes. The governing partial differential equations that we solve are the electroneutral Navier-Stokes-Onsager-Stefan-Maxwell (NSOSM) equations, which model momentum transport, multicomponent diffusion and electrical effects within the electrolyte. Our algorithms can be applied in the steady and transient settings, in two and three spatial dimensions, and under a variety of boundary conditions. Moreover, we allow for the material parameters (e.g. viscosity, diffusivities, thermodynamic factors and density) to be solution-dependent and thermodynamically non-ideal. The flexibility of our approach requires us to address subtleties that arise in the governing equations due to the interplay between boundary conditions and the equation of state. We demonstrate the algorithms in various physical configurations, including (i) electrolyte flow around a microfluidic rotating disk electrode and (ii) the flow in a Hull cell of a cosolvent electrolyte mixture used in lithium-ion batteries.

翻译：我们提出了一族广泛的高阶有限元算法，用于模拟电中性电解质的流动。所求解的控制偏微分方程为电中性纳维-斯托克斯-昂萨格-斯蒂芬-麦克斯韦（NSOSM）方程组，该方程组描述了电解质内部的动量输运、多组分扩散及电效应。我们的算法可应用于稳态与瞬态情形、二维与三维空间维度，并适用于多种边界条件。此外，我们允许材料参数（如粘度、扩散系数、热力学因子和密度）依赖于解且具有热力学非理想性。我们方法的灵活性要求我们处理控制方程中因边界条件与状态方程相互作用而产生的微妙问题。我们在多种物理构型中验证了该算法，包括：（i）微流体旋转圆盘电极周围的电解质流动，以及（ii）锂离子电池所用共溶剂电解质混合物在赫尔槽中的流动。