  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.
