A novel p-harmonic descent approach applied to fluid dynamic shape optimization
A novel p-harmonic descent approach applied to fluid dynamic shape optimization
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DOI：
10.1007/s00158-021-03030-x
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发表时间：
2021-03
影响因子：
3.9
通讯作者：
P. Müller;Niklas Kühl;Martin Siebenborn;K. Deckelnick;M. Hinze;T. Rung
中科院分区：
文献类型：
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作者：
P. Müller;Niklas Kühl;Martin Siebenborn;K. Deckelnick;M. Hinze;T. Rung
在流体力学应用中，我们提出了一种新的方法来实现非参数化形状的形状优化，即在拉普拉斯函数的帮助下使用形状导数来确定变形场。这种方法与拓扑中形状泛函的最陡峭下降方向的计算密切相关，并参考了Deckelnick等人最近发表的一篇文章（一种利用Lipschitz域进行形状优化的新方法，2021年），其中提出了这种想法。我们的方法被证明与最小拖曳自由浮动体相关的形状优化。从优化算法的收敛性、得到的形状以及大变形后计算网格的质量等方面对现有方法进行了验证。我们的数值结果强烈表明，与拓扑相关的形状优化-尽管在数值上要求更高-似乎优于调用希尔伯特空间方法的经典方法，涉及收敛性，获得的形状和大变形后的网格质量，特别是当最优形状具有尖角时。
We introduce a novel method for the implementation of shape optimization for non-parameterized shapes in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of theLaplacian for. This approach is closely related to the computation of steepest descent directions of the shape functional in thetopology and refers to the recent publication Deckelnick et al. (A novelapproach to shape optimisation with Lipschitz domains, 2021), where this idea is proposed. Our approach is demonstrated for shape optimization related to drag-minimal free floating bodies. The method is validated against existing approaches with respect to convergence of the optimization algorithm, the obtained shape, and regarding the quality of the computational grid after large deformations. Our numerical results strongly indicate that shape optimization related to the-topology—though numerically more demanding—seems to be superior over the classical approaches invoking Hilbert space methods, concerning the convergence, the obtained shapes and the mesh quality after large deformations, in particular when the optimal shape features sharp corners.