Well‐Posed Stokes/Brinkman and Stokes/Darcy Problems for Coupled Fluid‐Porous Viscous Flows
Well‐Posed Stokes/Brinkman and Stokes/Darcy Problems for Coupled Fluid‐Porous Viscous Flows
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耦合流体-多孔粘性流的适定斯托克斯/布林克曼和斯托克斯/达西问题
DOI：
10.1063/1.3498412
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
P. Angot
中科院分区：
文献类型：
--
作者：
P. Angot
本文提出了一类Stokes/Brinkman问题的适定模型，该模型具有一族跳跃嵌入边界条件（J. E. B.C.）在弱规则性假设下的浸入界面上。它是从最近提出的虚拟域问题的一般框架。我们的模型是基于代数传输条件相结合的应力和速度跳跃的接口$\Sigma$分离的流体和多孔域。这些条件，以及选择得到的运营商的bavivity，是足够普遍的，以获得通常的浸入边界条件$\Sigma$时，虚构的域的方法有关：斯蒂芬一样，罗宾（傅立叶），诺依曼或狄利克雷.此外，一般框架允许证明一些模型的物理相关的应力或速度跳跃边界条件的动量输运在流体-多孔界面的全局可解性。通过渐近分析证明了Ochoa-Tapia & Whitaker（1995）界面条件下的Stokes/Brinkman问题和Beavers & Joseph（1967）界面条件下的Stokes/Darcy问题都是适定的。据我们所知，只有Saffman（1971）近似界面条件下的Stokes/Darcy问题是适定的。
We present a well-posed model for the Stokes/Brinkman problem with a family of jump embedded boundary conditions (J.E.B.C.) on an immersed interface with weak regularity assumptions. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface $\Sigma$ separating the fluid and porous domains. These conditions, well chosen to get the coercivity of the operator, are sufficiently general to get the usual immersed boundary conditions on $\Sigma$ when fictitious domain methods are concerned: Stefan-like, Robin (Fourier), Neumann or Dirichlet... Moreover, the general framework allows to prove the global solvability of some models with physically relevant stress or velocity jump boundary conditions for the momentum transport at a fluid-porous interface. The Stokes/Brinkman problem with Ochoa-Tapia & Whitaker (1995) interface conditions and the Stokes/Darcy problem with Beavers & Joseph (1967) conditions are both proved to be well-posed by an asymptotic analysis. Up to our knowledge, only the Stokes/Darcy problem with Saffman (1971) approximate interface conditions was known to be well-posed.