Topology optimization of three-phase interpolation models in Darcy-stokes flow
Topology optimization of three-phase interpolation models in Darcy-stokes flow
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DOI：
10.1007/s00158-017-1836-8
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发表时间：
2018-04
影响因子：
3.9
通讯作者：
Chao Shen;L. Hou;E. Zhang;Jiahe Lin
中科院分区：
文献类型：
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作者：
Chao Shen;L. Hou;E. Zhang;Jiahe Lin
本文将流体流动的拓扑优化（TO）方法扩展到设计三相（即固体、流体和多孔材料）插补方案。除了对Darcy-Stokes方程控制区域的优化布局进行了大量的研究外，本文的目标是最小化多相插值模型中的压力衰减。在考虑流体通过多孔介质和不可穿透内壁（固相）的情况下，忽略浮力和其他外力，得到了最优分布。每个材料阶段分配两个设计变量，通过正则插值函数投影到元素空间中。将固体各向同性材料惩罚插值函数（SIMP）应用于Darcy-Stokes流的to过程中，该插值函数最初是为了最小化多种结构材料的柔度而开发的。将字段划分为设计域和非设计域，并组装TO布局以满足给定的性能功能。利用平滑的Heaviside投影滤波器和基于helmholtz型偏微分方程（PDE）的滤波器产生连续to过程的离散解。数值研究验证了所提出的插值方案。
This paper extends the topology optimization (TO) methods of fluid flows to design the three-phase (i.e. solid, fluid and porous materials) interpolation scheme. In addition to numerous studies about the optimized layout of regions governed by Darcy-Stokes equations, this paper aims to minimize the pressure attenuation in multiple phase interpolation models. The optimized distribution is obtained by considering both the fluid permeability through the porous media and impenetrable inner walls (solid phase) and neglecting buoyancy and other external body forces. Each material phase is assigned with two design variables that are projected into the element space via the regularized interpolation functions. The solid isotropic material with penalization (SIMP) interpolation functions, which is initially developed for minimizing compliance of multiple structural materials, is applied to TO processes of Darcy–Stokes flow. The fields are divided into the design and non-design domains, and TO layouts are assembled to satisfy the given performance functions. The smoothed Heaviside projection filter and Helmholtz-type Partial Differential Equation (PDE) based filter are utilized to produce discrete solutions in the continuum TO processes. Numerical studies are carried out to verify the proposed interpolation scheme.