In topology optimization of fluid-dependent problems, there is a need to interpolate within the design domain between fluid and solid in a continuous fashion. In density-based methods, the concept of inverse permeability in the form of a volumetric force is utilized to enforce zero fluid velocity in non-fluid regions. This volumetric force consists of a scalar term multiplied by the fluid velocity. This scalar term takes a value between two limits as determined by a convex interpolation function. The maximum inverse permeability limit is typically chosen through a trial and error analysis of the initial form of the optimization problem; such that the fields resolved resemble those obtained through an analysis of a pure fluid domain with a body-fitted mesh. In this work, we investigate the dependency of the maximum inverse permeability limit on the mesh size and the flow conditions through analyzing the Navier-Stokes equation in its strong as well as discretized finite element forms. We use numerical experiments to verify and characterize these dependencies.

翻译：在流体依赖问题的拓扑优化中，需要在设计域内以连续方式对流体与固体进行插值。在密度基方法中，利用体积力形式的逆渗透率概念来强制非流体区域中的流体速度为零。该体积力由一个标量项乘以流体速度构成。该标量项的值由凸插值函数确定，介于上下限之间。通常通过对优化问题的初始形式进行试错分析来选择最大逆渗透率限值，使得解算的场域与通过体适应网格分析纯流体域获得的结果相似。本文通过分析强形式及离散有限元形式的纳维-斯托克斯方程，研究了最大逆渗透率限值对网格尺寸和流动条件的依赖性。我们使用数值实验验证并表征了这些依赖关系。