Open Access

ARTICLE

Shape Optimization in Time-Dependent Navier-Stokes Flows via Function Space Parametrization Technique¹

Zhiming Gao², Yichen Ma³

1 This work is supported by the National Natural Science Fund of China under grant number 11001025.
2 Corresponding author. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing, P. R. China, 100088. Email: gao@iapcm.ac.cn.
3 School of Science, Xi’an Jiaotong University, Shaanxi, P.R. China, 710049. Email: ycma@mail.xjtu.edu.cn.

Computer Modeling in Engineering & Sciences 2010, 66(2), 135-164. https://doi.org/10.3970/cmes.2010.066.135

Abstract

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.

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Keywords

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