Mesh Deformation using Radial Basis Functions for Gradient-based Aerodynamic Shape Optimization
Mesh Deformation using Radial Basis Functions for Gradient-based Aerodynamic Shape Optimization
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DOI：
10.1016/j.compfluid.2006.11.002
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发表时间：
2007-07
影响因子：
2.8
通讯作者：
S. Jakobsson;O. Amoignon
中科院分区：
文献类型：
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作者：
S. Jakobsson;O. Amoignon
使用计算流体动力学（CFD）的基于惯性的气动外形优化以及气动弹性中的时间相关问题（即计算结构力学（CSM）和CFD之间的耦合计算）需要CFD网格的重复变形。基于径向基函数（RBF）的插值方案的设计，以传播的变形从边界到内部的CFD网格。与通常的拉普拉斯光顺方法相比，该方法可以减少网格变形所带来的计算量。此外，该算法是独立的网格连通性。因此，结构化和非结构化网格以及混合网格被同等对待。文中还详细研究了该插值格式在气动外形优化问题中的应用。当通过基于梯度的算法执行优化时，成本函数相对于设计参数被微分，以便获得梯度。通过求解从离散化的流动方程导出的某个伴随方程，最有效和精确地计算梯度。梯度的计算，这是详细介绍，涉及到网格变形的雅可比矩阵。最后，我们提出的ONERA M6机翼在跨音速使用插值算法的优化结果。结果用于与另一种网格变形技术进行比较。通过新算法得到的网格质量，和插值误差，相对于插值方案的参数：RBF的类型，RBF的形状参数，和控制点集进行了分析。
Gradient-based aerodynamic shape optimization using computational fluid dynamics (CFD), and time dependent problems in aeroelasticity, that is, coupled calculations between computational structural mechanics (CSM) and CFD, require repeated deformations of the CFD mesh. An interpolation scheme, based on radial basis functions (RBF), is devised in order to propagate the deformations from the boundaries to the interior of the CFD mesh. This method can lower the computational costs due to the deformation of the mesh, in comparison with the usual Laplace smoothing. Moreover, the algorithm is independent of the mesh connectivities. Therefore, structured and unstructured meshes are equally treated as well as hybrid meshes. The application of this interpolation scheme in problems of aerodynamic shape optimization is also carefully investigated. When the optimization is executed by a gradient-based algorithm the cost function is differentiated with respect to the design parameters in order to obtain the gradient. The gradient is most efficiently and accurately calculated by solving a certain adjoint equation derived from the discretized flow equations. The calculation of the gradient, which is detailed in this presentation, involves the Jacobian matrix of the mesh deformation. Finally, we present the results of an optimization of the ONERA M6 wing at transonic speed using the interpolation algorithm. The results are used for comparison with another technique of mesh deformation. The quality of the mesh obtained by the new algorithm, and the interpolation error, are analyzed with respect to the parameters of the interpolation scheme: the type of RBF, the RBF’s shape parameter, and the sets of control points.