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.

翻译：金属-电解液反应的数值模拟是理解和预测广泛物理现象的核心，然而由于反应速率差异引发的数值振荡，这一过程常面临挑战。氢向金属中的渗入是典型的技术相关现象，其模拟因反应项刚度而受到制约：由于反应速率跨越多个数量级，这严重限制了时间增量的大小。本研究提出一种针对电化学界面反应的集总积分格式，该格式不受数值振荡影响。该格式以一致方式积分反应项，同时解耦相邻节点，使得在无振荡或收敛问题的条件下可采用更大的时间增量。通过模拟不同反应速率常数与环境条件下的氢渗入过程，验证了该格式的稳定性与潜力。以往的氢吸收预测仅能限于分钟级时间尺度，而本文提出的集总积分格式使得模拟可跨越数十年时间尺度，从而能够达到稳态条件，并对实际应用相关时间尺度下的氢渗入进行量化。