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首页> 外文期刊>Journal of Computational Physics >A variational level set method for the topology optimization of steady-state Navier-Stokes flow
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A variational level set method for the topology optimization of steady-state Navier-Stokes flow

机译：稳态Navier-Stokes流的拓扑优化变分级别方法

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The smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density-based approaches, though well established in structural designs, inadequate. This paper presents a level-set method for topology optimization of steady-state Navier-Stokes flow subject to a specific fluid volume constraint. The solid-fluid interface is implicitly characterized by a zero-level contour of a higher-order scalar level set function and can be naturally transformed to other configurations as its host moves. A variational form of the cost function is constructed based upon the adjoint variable and Lagrangian multiplier techniques. To satisfy the volume constraint effectively, the Lagrangian multiplier derived from the first-order approximation of the cost function is amended by the bisection algorithm. The procedure allows evolving initial design to an optimal shape and/or topology by solving the Hamilton-Jacobi equation. Two classes of benchmarking examples are presented in this paper: (1) periodic microstructural material design for the maximum permeability; and (2) topology optimization of flow channels for minimizing energy dissipation. A number of 2D and 3D examples well demonstrated the feasibility and advantage of the level-set method in solving fluid-solid shape and topology optimization problems. Crown Copyright (C) 2008 Published by Elsevier Inc. All rights reserved.
机译：拓扑界面的平滑度通常很大程度上影响了流体优化，有时会使基于密度的方法，但在结构设计中很好地建立，不足。本文介绍了稳态Navier-Stokes流量的拓扑优化水平集合，经过特定的流体体积约束。固体流体接口通过高阶标量级集功能的零电平轮廓隐式表征，并且可以在其主机移动时自然地转换为其他配置。基于伴随变量和拉格朗日乘法器技术构建成本函数的变分形式。为了有效地满足体积约束，通过双分算法修正了从成本函数的一阶近似的拉格朗日乘数。该过程允许通过求解Hamilton-Jacobi方程来使初始设计与最佳形状和/或拓扑。本文提出了两类基准测试示例：（1）定期微观结构材料设计，用于最大渗透性; （2）流动通道的拓扑优化，以最大限度地减少能量耗散。许多2D和3D示例良好地证明了求解流体 - 固体形状和拓扑优化问题的水平设定方法的可行性和优势。 Crown版权（c）2008由elsevier公司发布的所有权利保留。

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