Shape Optimization of an Oscillating Body in Fluid Flow by Adjoint Equation and ALE Finite Element Methods
Shape Optimization of an Oscillating Body in Fluid Flow by Adjoint Equation and ALE Finite Element Methods
复制标题
流体流动中振动体形状的伴随方程和ALE有限元方法优化
DOI：
10.48550/arxiv.2312.03447
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发表时间：
2007
期刊：
影响因子：
2.3
通讯作者：
M. Kawahara
中科院分区：
文献类型：
--
作者：
Hiroki Yoshida;M. Kawahara
本研究的目的是利用任意拉格朗日欧拉有限元法和以阻力和升力表示性能函数的最优控制理论，确定瞬态不可压缩粘性流体中振荡体的最小阻力和升力形状。在满足状态方程和等体积条件下，性能函数最小。利用拉格朗日乘子法可将该问题转化为无约束条件的最小化问题。利用伴随方程和梯度法对体形进行更新。在本研究中，采用加权梯度法作为最小化技术。最终得到的形状，阻力和升力分别降低了66.2%和92.8%。并与非振动体的最终形状进行了比较。得到了振荡体的最终形状，该形状与非振荡体有很大的不同。
The purpose of this study is to determine the minimum drag and lift shape of an oscillating body located in the transient incompressible viscous fluid flow by the Arbitrary Lagrangian Eulerian finite element method and an optimal control theory in which a performance function is expressed by the drag and lift forces. The performance function should be minimized satisfying the state equation and constant volume condition. This problem can be transformed into the minimization problem without constraint condition by the Lagrange multiplier method. The adjoint equation and gradient are used to the renewal of shape of the body. In this study, as a minimization technique, the weighted gradient method is applied. The final shape is obtained of which drag and lift forces are reduced by 66.2 % and 92.8 %, respectively. The final shape obtained by this study is compared with the final shape of the non-oscillating body. The final shape of the oscillating body is obtained which is significantly different from the non-oscillating body.