Shape Optimization in Time-Dependent Navier-Stokes Flows via Function Space Parametrization Technique
Shape Optimization in Time-Dependent Navier-Stokes Flows via Function Space Parametrization Technique
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DOI：
10.3970/cmes.2010.066.135
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发表时间：
2010-09
影响因子：
2.4
通讯作者：
Zhiming Gao;Yi-chen Ma
中科院分区：
文献类型：
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作者：
Zhiming Gao;Yi-chen Ma
形状优化技术在分布参数系统流体力学问题中发挥着越来越重要的作用。本文研究了由含时N-S方程控制的二维粘性流动的形状优化问题。在流体域中建立了粘性耗散能的最小化问题。利用鞍点形式的可微性和函数空间的参数化技巧，我们得到了代价泛函的连续形状梯度的结构。最后，将一种具有网格自适应和网格移动策略的梯度型算法成功地应用于实际工程中。
Shape optimization technique has an increasing role in fluid dynamics problems governed by distributed parameter systems. In this paper, we present the problem of shape optimization of two dimensional viscous flow governed by the time dependent Navier–Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. We derive the structure of continuous shape gradient of the cost functional by using the differentiability of a saddle point formulation with a function space parametrization technique. Finally a gradient type algorithm with mesh adaptation and mesh movement strategies is successfully and efficiently applied.