Stokes-Darcy耦合问题的扩散界面法分析

IF 1.9 3区 数学 Q2 Mathematics
Martina Bukavc, B. Muha, A. Salgado
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引用次数: 0

摘要

我们考虑自由流动的流体和多孔介质流动之间的相互作用,其中自由流动的流体使用时间相关的斯托克斯方程来描述,而多孔介质流动在原始公式中使用达西定律来描述。为了在数值上解决这个问题,我们使用了扩散界面方法,其中耦合问题的弱形式写在包含Stokes和Darcy区域的扩展域上。这是通过一个相场函数来实现的,该函数在Stokes区域等于1,在Darcy区域等于0,并且在Stokes-Darcy界面周围宽度为O(λ)的扩散区域上,这两个值之间可以平滑地转换。我们证明了扩散界面公式对标准、锐界面公式的收敛性,并推导了收敛率。这是通过推导漫射界面方法离散化的先验误差估计,以及在连续水平上分析漫射界面方法的建模误差来实现的。通过数值算例给出了收敛速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analysis of a diffuse interface method for the Stokes-Darcy coupled problem
We consider the interaction between a free flowing fluid and a porous medium flow, where the free flowing fluid is described using the time dependent Stokes equations, and the porous medium flow is described using Darcy’s law in the primal formulation. To solve this problem numerically, we use a diffuse interface approach, where the weak form of the coupled problem is written on an extended domain which contains both Stokes and Darcy regions. This is achieved using a phase-field function which equals one in the Stokes region and zero in the Darcy region, and smoothly transitions between these two values on a diffuse region of width O(ϵ) around the Stokes-Darcy interface. We prove convergence of the diffuse interface formulation to the standard, sharp interface formulation, and derive rates of convergence. This is performed by deriving a priori error estimates for discretizations of the diffuse interface method, and by analyzing the modeling error of the diffuse interface approach at the continuous level. The convergence rates are also shown computationally in a numerical example.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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