arXiv subjects
Publications and source records attributed to Florian Oschmann.
We consider the time-dependent compressible Navier--Stokes equations in the low Mach number regime in a family of domains $Ω_ε\subset R^d$ converging in the sense of Mosco to a domain $Ω\subset R^d$, $d \in \{2,3\}$. We show the limit is the incompressible Navier--Stokes system in $Ω$.
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 the particle size scaling like $\varepsilon^α$ with $α\in (1,3)$.
We analyze behavior of weak solutions to compressible fluid flows in a bounded domain in $\mathbb{R}^3$, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like $\varepsilon^α$, $α> 3$, with $\varepsilon$ denoting the average distance between the balls, the problem homogenize with the same limiting equation. Our main contribution is a construction of the Bogovski\uı operator, uniformly in $\varepsilon$, without any assumptions on the minimal distance between the balls.
We consider the homogenization of the compressible Navier-Stokes-Fourier equations in a randomly perforated domain in $\mathbb{R}^3$. Assuming that the particle size scales like $\varepsilon^α$, where $\varepsilon>0$ is their mutual distance and $α>3$, we show that in the limit $\varepsilon\to 0$, the velocity, density, and temperature converge to a solution of the same system. We follow the methods of Lu and Pokorný [https://doi.org/10.1016/j.jde.2020.10.032], where they considered the full system in periodically perforated domains.