不定常Navier-Stokes流的形状优化设计
Optimal Shape Design for the Time-dependent Navier--Stokes Flow
摘要：
本文研究了由不定常Navier-斯托克斯方程控制的二维流动的形状优化问题。我们推导出形状梯度的结构相对于形状的可变域的不定常成本泛函通过使用状态导数相对于形状的流体域及其相关的伴随状态。最后，我们将梯度型算法应用到我们的问题中，数值例子表明我们的理论是有用的，所提出的算法在低雷诺数流动中是可行的。
英文摘要：
This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for time-dependent cost functionals by using the state derivative with respect to the shape of the fluid domain and its associated adjoint state. Finally we apply a gradient type algorithm to our problem and numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible in low Reynolds number flow.
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