论文标题
在Brinkman类型的薄多孔介质域中的两相流问题的极限
On the limit of a two-phase flow problem in thin porous media domains of Brinkman-type
论文作者
论文摘要
我们研究了Brinkman类型的薄多孔培养基领域中的两相流的过程。这通常是由耦合的，混合型微分方程的流体饱和度和压力的模型来描述的。为了降低模型的复杂性，已经提出了使用域薄几何形状的不同方法。 我们专注于简化的模型，该模型被公式为单个非局部进化方程。它是通过将标准渐近分析应用于无量纲耦合模型来得出的，但是，仍然缺乏刚性的数学推导。在本文中，我们证明还原模型是耦合两相流模型的分析限制，因为域的宽度比率的几何参数趋向于零。确切地说，随着几何参数接近零，我们证明了耦合模型的弱解的收敛性。
We study the process of two-phase flow in thin porous media domains of Brinkman-type. This is generally described by a model of coupled, mixed-type differential equations of fluids' saturation and pressure. To reduce the model complexity, different approaches that utilize the thin geometry of the domain have been suggested. We focus on a reduced model that is formulated as a single nonlocal evolution equation of saturation. It is derived by applying standard asymptotic analysis to the dimensionless coupled model, however, a rigid mathematical derivation is still lacking. In this paper, we prove that the reduced model is the analytical limit of the coupled two-phase flow model as the geometrical parameter of domain's width--length ratio tends to zero. Precisely, we prove the convergence of weak solutions for the coupled model to a weak solution for the reduced model as the geometrical parameter approaches zero.
