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.
翻译:2D 的特性方法。 对于这个局部差异方程式系统,特征曲线似乎是流体图和适用于流体的理论众所周知的C+和C-曲线。在2D 的流体图上满足的差异方程式随后以3D 的线性组合来扩展和演示。这些结果扩展了直接系统众所周知的对等方,并且应当用于对连接字段或敏感问题的完美流模型的分析和可能的数字研究。除了分析理论外,结果还表现在离2D流场和双相联场的兼容性关系在空气油非常精细的网格上的数值整合。