论文标题
在不断发展的多孔培养基中，局部存在用于微麦克罗模型的强大解决方案
Local existence of strong solutions to micro-macro models for reactive transport in evolving porous media
论文作者
论文摘要
两尺度模型在模拟不断发展的多孔介质中的反应流和传输方面采用了一种有希望的方法。从经典上讲，同质流和传输方程在宏观尺度上求解，而有效参数是从可能不断发展的参考几何形状（微尺度）的辅助细胞问题获得的。尽管在渲染实验室/现场尺度模拟的计算上是可行的，但关于可行的分析结果，关于出现的两尺度双侧耦合系统的分析结果通常限于简化模型。在本文中，我们首先得出了从基础几何形状到宏观量的部分耦合的平滑依赖性结果。因此，代表性流体结构域的改变由差异的平滑路径描述。利用有效的空间和时间依赖性宏观系数的规律性，我们使用固定点参数为部分耦合的微麦克罗系统提出了局部时间的存在结果。更重要的是，我们将结果扩展到双侧耦合扩散传输模型，包括对不断发展的几何形状的级别描述。
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are obtained from auxiliary cell problems on possibly evolving reference geometries (micro-scale). Despite their perspective success in rendering lab/field-scale simulations computationally feasible, analytic results regarding the arising two-scale bilaterally coupled system often restrict to simplified models. In this paper, we first derive smooth-dependence results concerning the partial coupling from the underlying geometry to macroscopic quantities. Therefore, alterations of the representative fluid domain are described by smooth paths of diffeomorphisms. Exploiting the gained regularity of the effective space- and time-dependent macroscopic coefficients, we present local-in-time existence results for strong solutions to the partially coupled micro-macro system using fixed-point arguments. What is more, we extend our results to the bilaterally coupled diffusive transport model including a level-set description of the evolving geometry.
