Abstract This article shows how to consistently and accurately manage the Lagrangian formulation of chemical reaction equations coupled with the superficial velocity formalism introduced in the late 80s by Quintard and Whitaker. Lagrangian methods prove very helpful in problems in which transport effects are strong or dominant, but they need to be periodically put back in a regular lattice, a process called remeshing. In the context of digital rock physics, we need to ensure positive concentrations and regularity to accurately handle stagnation point neighborhoods. These two conditions lead to the use of kernels resulting in extra-diffusion, which can be prohibitively high when the diffusion coefficient is small. This is the case especially for reactive porous media, and the phenomenon is reinforced in porous rock matrices due to Archie’s law. This article shows how to overcome this difficulty in the context of a two-scale porosity model applied in the Darcy-Brinkman-Stokes equations, and how to obtain simultaneous sign preservation, regularity and accurate diffusion, and apply it to dissolution processes at the pore scale of actual rocks.

中文翻译：

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用于模拟孔隙尺度溶解过程的重新网格化拉格朗日方法的改进

摘要 本文展示了如何一致且准确地管理化学反应方程的拉格朗日公式以及 Quintard 和 Whitaker 在 80 年代后期引入的表面速度形式。拉格朗日方法证明在传输效应很强或占主导地位的问题中非常有用，但它们需要定期放回规则晶格中，这个过程称为重新网格化。在数字岩石物理的背景下，我们需要确保正浓度和规律性以准确处理驻点邻域。这两个条件导致使用内核导致额外扩散，当扩散系数很小时，这可能会高得令人望而却步。对于反应性多孔介质尤其如此，并且由于阿奇定律，这种现象在多孔岩石基质中得到加强。