A scalable DG solver for the electroneutral Nernst-Planck equations

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 Peclet 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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The simulation of flowing electrochemical systems is becoming increasingly important in the context of intermittent renewable energy and electrochemical technologies. The high Peclet regime of many applications makes off-the-shelf discretization methods unsuitable. This work presents a high-order Discontinuous Galerkin scheme specifically designed for the electroneutral Nernst-Planck equations. The scheme incorporates charge conservation formulation and different treatments for advection, migration, diffusion, and electric potential.