论文标题
伴随Euler方程的普通微分方程
Ordinary differential equations for the adjoint Euler equations
论文作者
论文摘要
首先，使用2D中的特征方法来得出了伴随欧拉方程的普通微分方程。对于这种部分差异方程的系统，特征曲线似乎是应用于流动的理论的流轨道和众所周知的C+和C曲线。然后，通过原始伴随方程的线性组合扩展并在3D中扩展并证明沿2D中的流trace所满足的微分方程。这些发现扩展了其众所周知的直接系统，并应针对伴随领域或灵敏度问题提供分析性和可能的数值研究。除了分析理论之外，结果是通过在围绕机翼的非常细的网格上的离散2D流场和双一致性的伴奏场的兼容性整合来证明的。
Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and the well-known C+ and C- curves of the theory applied to the flow. The differential equations satisfied along the streamtraces in 2D are then extended and demonstrated in 3D by linear combinations of the original adjoint equations. These findings extend their well-known counterparts for the direct system, and should serve analytical and possibly numerical studies of the perfect-flow model with respect to adjoint fields or sensitivity questions. Beside the analytical theory, the results are demonstrated by the numerical integration of the compatibility relationships for discrete 2D flow-fields and dual-consistent adjoint fields over a very fine grid about an airfoil.
