SIAM Journal on Scientific Computing, Volume 43, Issue 5, Page B1081-B1104, January 2021.
The sensitivity equation method aims at estimating the derivative of the solution of partial differential equations with respect to a parameter of interest. The objective of this work is to investigate the ability of an isogeometric discontinuous Galerkin (DG) method to evaluate accurately sensitivities with respect to shape parameters originating from computer-aided design (CAD) in the context of compressible aerodynamics. The isogeometric DG method relies on nonuniform rational B-spline representations, which allows us to define a high-order numerical scheme for Euler/Navier--Stokes equations, fully consistent with CAD geometries. We detail how this formulation can be exploited to construct an efficient and accurate approach to evaluate shape sensitivities. A particular attention is paid to the treatment of boundary conditions for sensitivities, which are more tedious in the case of geometrical parameters. The proposed methodology is first verified on a test-case with an analytical solution and then applied to two more demanding problems that concern the inviscid flow around an airfoil with its camber as a shape parameter and the unsteady viscous flow around a three-element airfoil with the positions of slat and flap as parameters.

中文翻译：

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使用等几何不连续伽辽金方法进行空气动力学形状敏感性分析

SIAM 科学计算杂志，第 43 卷，第 5 期，第 B1081-B1104 页，2021 年 1 月。
灵敏度方程方法旨在估计偏微分方程解对感兴趣参数的导数。这项工作的目的是研究等几何不连续伽辽金 (DG) 方法在可压缩空气动力学背景下准确评估源自计算机辅助设计 (CAD) 的形状参数的灵敏度的能力。等几何 DG 方法依赖于非均匀有理 B 样条表示，这使我们能够为 Euler/Navier-Stokes 方程定义高阶数值方案，与 CAD 几何完全一致。我们详细介绍了如何利用这种公式来构建一种有效且准确的方法来评估形状敏感性。特别注意处理敏感性的边界条件，这在几何参数的情况下更加乏味。所提出的方法首先在带有解析解的测试用例上得到验证，然后应用于两个更苛刻的问题，这些问题涉及以弯度为形状参数的翼型周围的无粘性流动和三元翼型周围的非定常粘性流动。缝翼和襟翼的位置作为参数。