标题： 伴随和直接特征方程用于二维可压缩欧拉流 显示英文标题

标题： Adjoint and direct characteristic equations for two-dimensional compressible Euler flows

摘要： 特征线方法是用于理解偏微分方程解的经典方法。它最近被应用于二维欧拉方程的伴随方程，本文的第一个目标是提出一种线性代数分析，大大简化沿特征曲线族满足的独立特征方程数量的讨论。该方法可以同时应用于直接问题和伴随问题，本文的第二个目标是直接在保守变量中推导出二维可压缩无粘流的特征方程。最后，通过一个经典格式及其对偶一致离散伴随对理论结果进行了评估。 显示英文摘要

摘要： 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.