论文标题
达西定律是穿孔域中可压缩流体的低马赫和同质化极限
Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
论文作者
论文摘要
我们考虑了由定期分布的相同粒子穿孔的三维结构域中可压缩的正压纳维尔 - 长方形方程的均匀限制。我们研究粒径和距离的状态，使颗粒的体积分数趋于零，但它们的电阻密度趋于无穷大。假设马赫数随着一定速率的增加而增加，则微观系统的重新速度和压力会收敛到达西定律给出的有效方程的解决方案。我们认为的颗粒尺寸范围完全相同，这在不可压缩的流体的均匀限制下导致了达西定律。与Darcy制度的先前结果不同，我们估计了通过Bogovski \ u {ı}操作员与压力近似相关的赤字，这允许对Lebesgue和Sobolev空间中的压力进行更灵活的估计，并允许证明所有Barotropicentent $γ> \ frac32 $。
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is increasing with a certain rate, the rescaled velocity and pressure of the microscopic system converges to the solution of an effective equation which is given by Darcy's law. The range of sizes of particles we consider are exactly the same which lead to Darcy's law in the homogenization limit of incompressible fluids. Unlike previous results for the Darcy regime we estimate the deficit related to the pressure approximation via the Bogovski\u{ı} operator This allows for more flexible estimates of the pressure in Lebesgue and Sobolev spaces and allows to proof convergence results for all barotropic exponents $γ> \frac32$.
