A scalable DG solver for the electroneutral Nernst-Planck equations

TL;DR

This paper introduces a high-order Discontinuous Galerkin method for efficiently simulating electroneutral Nernst-Planck equations in high Péclet regimes, enabling scalable and accurate electrochemical system modeling.

Contribution

It presents a novel high-order DG scheme with tailored charge conservation formulation and preconditioning strategies for large-scale 3D electrochemical simulations.

Findings

Demonstrates convergence of the discretization scheme.

Shows strong scaling performance for large 3D problems.

Validates the method's effectiveness in high Péclet regimes.

Abstract

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.