The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The high P\'eclet regime of many such applications prevents the use of off-the-shelf discretization methods. In this work, we present a high-order Discontinuous Galerkin scheme for the electroneutral Nernst-Planck equations. The chosen charge conservation formulation allows for the specific treatment of the different physics: upwinding for advection and migration, and interior penalty for diffusion of ionic species as well the electric potential. Similarly, the formulation enables different treatments in the preconditioner: AMG for the potential blocks and ILU-based methods for the advection-dominated concentration blocks. We evaluate the convergence rate of the discretization scheme through numerical tests. Strong scaling results for two preconditioning approaches are shown for a large 3D flow-plate reactor example.
翻译:由于间歇性可再生能源与电化学技术(例如能源储存和化学制造)之间的协同作用,对流动电化学系统进行稳健、可伸缩的模拟越来越重要。许多此类应用的高P\'分类制度防止使用现成的离散方法。在这项工作中,我们为电子中性Nernst-Planck方程式提出了一个高阶不连续的Galerkin计划。选择的电荷保护配方允许具体处理不同的物理学:吸附和和迁移,以及电离子物种扩散和电力潜力的内部惩罚。同样,该配方也使得先决条件中可以采用不同的处理方法:潜在区块的AMG和以国际液化铀为主的吸附聚物块的ILU方法。我们通过数字测试来评估离散办法的趋同率。大型的3D流压式反应堆示例显示了两种先决条件的放大效果。