论文标题
高粘性液体对刚性障碍物的近似
Approximation of rigid obstacle by highly viscous fluid
论文作者
论文摘要
在本文中，我们研究了有关在二维情况下由固定的Navier-Stokes方程支配的刚性障碍物近似的问题。这个想法是考虑到障碍物的高度粘性液体。正式地，随着流体粘度进入障碍物所占据的区域内部的无穷大，我们在极限内获得了原始问题。 主要目标是建立更好的近似解决方案的规律性。特别是，证明了速度梯度的点估计。 我们提供的数值证据表明，即使是相对较小的惩罚参数值，也可以合理地近似问题。
In this paper, we study the problem concerning the approximation of a rigid obstacle for flows governed by the stationary Navier-Stokes equations in the two-dimensional case. The idea is to consider a highly viscous fluid in the place of the obstacle. Formally, as the fluid viscosity goes to infinity inside the region occupied by the obstacle, we obtain the original problem in the limit. The main goal is to establish a better regularity of approximate solutions. In particular, the pointwise estimate for the gradient of the velocity is proved. We give numerical evidence that the penalized solution can reasonably approximate the problem, even for relatively small values of the penalty parameter.
