The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this paper is to present a linear algebra analysis that greatly simplifies the discussion of the number of independant characteristic equations satisfied along a family of characteristic curves. This method may be applied for both the direct and the adjoint problem and our second goal is to directly derive in conservative variables the characteristic equations of 2D compressible inviscid flows. Finally, the theoretical results are assessed for a nozzle flow with a classical scheme and its dual consistent discrete adjoint.

翻译：特征方法是一种经典方法，用于理解偏微分方程的解。该方法最近被应用于二维欧拉方程的伴随方程，本文的首要目标是提出一种线性代数分析，该分析极大地简化了沿一族特征曲线满足的独立特征方程数量的讨论。此方法可同时应用于直接问题和伴随问题，我们的第二个目标是直接在守恒变量中推导二维可压缩无粘流的特征方程。最后，通过一个使用经典格式及其对偶一致的离散伴随方程的喷管流动实例，验证了理论结果。