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Computational modelling of metal-electrolyte reactions is central to theunderstanding and prediction of a wide range of physical phenomena, yet this isoften challenging owing to the presence of numerical oscillations that arisedue to dissimilar reaction rates. The ingress of hydrogen into metals is aparadigmatic example of a technologically-relevant phenomenon whose simulationis compromised by the stiffness of the reaction terms, as reaction rates varyover orders of magnitude and this significantly limits the time increment size.In this work, we present a lumped integration scheme for electro-chemicalinterface reactions that does not suffer from numerical oscillations. Thescheme integrates the reactions in a consistent manner, while it also decouplesneighbouring nodes and allows for larger time increments to be used withoutoscillations or convergence issues. The stability and potential of our schemeis demonstrated by simulating hydrogen ingress over a wide range of reactionrate constants and environmental conditions. While previous hydrogen uptakepredictions were limited to time scales of minutes, the present lumpedintegration scheme enables conducting simulations over tens of years, allowingus to reach steady state conditions and quantify hydrogen ingress for timescales relevant to practical applications.

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