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:在对依赖液体的问题进行地形优化时,需要连续地在液体和固体之间的设计领域进行内插。在以密度为基础的方法中,以体积为形式的反渗透性概念被用于在非液体地区强制实施零液体速度。这种体积力是由液积乘以流体速度的斜度值乘以体积。这个斜度术语取两个极限之间的值,这两个界限由对流的内插函数决定。最大反渗透性限制通常是通过对优化问题的最初形式进行试验和错误分析来选择的;因此,解析的字段类似于通过分析一个纯液体领域而获得的以体装的网格。在这项工作中,我们通过分析坚固的纳维-斯托克斯方程式和离散的有限元素形式,来调查最大反渗透性限度对网格大小和流动条件的依赖性。我们用数字实验来核实和辨别这些依赖性。</s>