Stabilising effects of lumped integration schemes for the simulation of metal-electrolyte reactions

Computational modelling of metal-electrolyte reactions is central to the understanding and prediction of a wide range of physical phenomena, yet this is often challenging owing to the presence of numerical oscillations that arise due to dissimilar reaction rates. The ingress of hydrogen into metals is a paradigmatic example of a technologically-relevant phenomenon whose simulation is compromised by the stiffness of the reaction terms, as reaction rates vary over orders of magnitude and this significantly limits the time increment size. In this work, we present a lumped integration scheme for electro-chemical interface reactions that does not suffer from numerical oscillations. The scheme integrates the reactions in a consistent manner, while it also decouples neighbouring nodes and allows for larger time increments to be used without oscillations or convergence issues. The stability and potential of our scheme is demonstrated by simulating hydrogen ingress over a wide range of reaction rate constants and environmental conditions. While previous hydrogen uptake predictions were limited to time scales of minutes, the present lumped integration scheme enables conducting simulations over tens of years, allowing us to reach steady state conditions and quantify hydrogen ingress for time scales relevant to practical applications.