Darcy's law for a compressible thermofluid

Time-Asymptotics of Physical Vacuum Free Boundaries for Compressible Inviscid Flows with Damping

In this paper, we prove the leading term of time-asymptotics of the moving vacuum boundary for compressible inviscid flows with damping to be that for Barenblatt self-similar solutions to the corresponding porous media equations obtained by simplifying momentum equations via Darcy's law plus the possible shift due to the movement of the center of mass, in the one-dimensional and three-dimensional spherically symmetric motions, respectively. This gives a complete description of the large time asymptotic behavior of solutions to the corresponding vacuum free boundary problems. The results obtain…

Homogenization and low Mach number limit of compressible Navier-Stokes equations in critically perforated domains

In this note, we consider the homogenization of the compressible Navier-Stokes equations in a periodically perforated domain in $\mathbb{R}^3$. Assuming that the particle size scales like $\varepsilon^3$, where $\varepsilon>0$ is their mutual distance, and that the Mach number decreases fast enough, we show that in the limit $\varepsilon\to 0$, the velocity and density converge to a solution of the incompressible Navier-Stokes equations with Brinkman term. We strongly follow the methods of Höfer, Kowalczik and Schwarzacher [arXiv:2007.09031], where they proved convergence to Darcy's law for th…

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient…

穿孔区域中可压缩Navier-Stokes方程的双尺度收敛均匀化

Homogenization of the compressible Navier-Stokes equations via two-scale convergence in perforated domains

通过双尺度收敛方法，研究周期穿孔区域中可压缩等熵Navier-Stokes方程的均匀化，导出Darcy定律和孔隙介质方程，并建立密度强双尺度收敛，将绝热常数扩展到γ>9/5。

具有摩擦阻尼的随机可压缩欧拉方程：$L^\infty$ 马尔可夫解的存在性及渐近多孔介质类行为

Stochastic Compressible Euler Equations with Frictional Damping: Existence of $L^\infty$ Martingale Solutions and Asymptotic Porous Medium-Like Behavior

本文研究了一维等熵可压缩欧拉方程在线性摩擦阻尼作用下的随机行为，证明了$L^\infty$马尔可夫解的存在性，并展示了在合适噪声条件下解几乎必然且指数收敛到常稳态，其密度近似由确定性多孔介质方程的渐近解描述。

M维带阻尼可压缩Euler方程物理真空自由边界问题的整体存在性与Barenblatt型解的渐近等价性

Global Existence and Asymptotic Equivalence to Barenblatt-type Solutions for the Physical Vacuum Free Boundary Problem of Damped Compressible Euler Equations in M-D

本文证明了2D和3D带阻尼可压缩Euler方程物理真空自由边界问题的整体存在性，通过提升扰动时间导数的衰减率确保时间可积性，并证明其渐近等价于Barenblatt自相似解，同时统一了时间依赖与时间无关阻尼情形的处理。

Almost Global Solutions to the Three-dimensional Isentropic Inviscid Flows with Damping in Physical Vacuum Around Barenlatt Solutions

For the three-dimensional vacuum free boundary problem with physical singularity that the sound speed is $C^{ {1}/{2}}$-H$\ddot{\rm o}$lder continuous across the vacuum boundary of the compressible Euler equations with damping, without any symmetry assumptions, we prove the almost global existence of smooth solutions when the initial data are small perturbations of the Barenblatt self-similar solutions to the corresponding porous media equations simplified via Darcy's law. It is proved that if the initial perturbation is of the size of $ε$, then the existing time for smooth solutions is at lea…

通过重覆均质化方法得到的绝对刚体的双孔隙度模型

Double Porosity Models for Absolutely Rigid Body via Reiterated Homogenization

本文通过重覆均质化方法，推导了绝对刚体中液体过滤的双孔隙度模型，得到了长短时间过程对应的不同控制方程。