论文标题
分析使用Brinkman定律浸入粘性液体中的障碍
Analysis of obstacles immersed in viscous fluids using Brinkman's law for steady Stokes and Navier-Stokes equations
论文作者
论文摘要
从稳定的Stokes和Navier-Stokes模型中，几位作者考虑了一种惩罚方法，用于近似围绕障碍物的流体方程。在这项工作中，我们提出了一种使用虚拟域来研究通过简化的Brinkman定律的多孔媒体来研究不可压缩粘性液体中浸入不可压缩粘性液体的障碍的理由。如果标量函数$ψ$被认为是渗透性的倒数，则可以研究$ψ$的奇异性作为障碍物的近似值（当$ψ$倾向于$ \ infty $）或与流体相对应的域（当$ψ= 0 = 0 $或非常接近$ 0 $时）。研究了扰动问题对解决方案的强大收敛性，还考虑了取决于惩罚参数的误差估计，既是用Stokes和Navier-Stokes方程建模的具有不均匀边界条件的流体。提出了一个数值实验，该实验验证了这一结果，并允许研究这种扰动的流动问题模拟和障碍物的识别。
From the steady Stokes and Navier-Stokes models, a penalization method has been considered by several authors for approximating those fluid equations around obstacles. In this work, we present a justification for using fictitious domains to study obstacles immersed in incompressible viscous fluids through a simplified version of Brinkman's law for porous media. If the scalar function $ψ$ is considered as the inverse of permeability, it is possible to study the singularities of $ψ$ as approximations of obstacles (when $ψ$ tends to $\infty$) or of the domain corresponding to the fluid (when $ψ= 0$ or is very close to $0$). The strong convergence of the solution of the perturbed problem to the solution of the strong problem is studied, also considering error estimates that depend on the penalty parameter, both for fluids modeled with the Stokes and Navier-Stokes equations with inhomogeneous boundary conditions. A numerical experiment is presented that validates this result and allows to study the application of this perturbed problem simulation of flows and the identification of obstacles.
