论文标题
分析有限体积的离散伴随字段，用于二维可压缩欧拉流量
Analysis of finite-volume discrete adjoint fields for two-dimensional compressible Euler flows
论文作者
论文摘要
这项工作涉及与可压缩欧拉方程和经典空气动力学功能相关的离散和连续伴随字段的许多问题。离散伴随方程与相应连续伴随偏微分方程的一致性是其中之一。它已经建立或至少仅针对少数数字方案进行了讨论，本文的贡献是为了在以细胞中为中心的有限量公式中提供2D Jameson-Schmidt-Turkel方案的伴随一致性条件。从新的启发式角度研究了一致性问题，通过离散离散流和伴随字段的连续伴随方程来分散。两种观点都证明提供有用的信息。此外，经常注意到，离散或连续的无粘性升力和拖动伴随表现出靠近墙壁的数值差异，并为广泛的亚音速和跨性别流程条件而言，靠近墙壁和停滞流线。此处使用参考文献[Giles and Pierce，AIAA Paper 97-1850，1997]中引入的物理源术语扰动方法对此进行了分析。从这种角度来看，第四个物理源术语似乎是对此行为负责的唯一一个。还证明，伴随变量的数值差异对应于流动对停滞压力的对流增量的响应，以及在源处产生的熵的减小以及升力和阻力的结果变化。
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with the corresponding continuous adjoint partial differential equation is one of them. It is has been established or at least discussed only for a handful of numerical schemes and a contribution of this article is to give the adjoint consistency conditions for the 2D Jameson-Schmidt-Turkel scheme in cell-centred finite-volume formulation. The consistency issue is also studied here from a new heuristic point of view by discretizing the continuous adjoint equation for the discrete flow and adjoint fields. Both points of view prove to provide useful information. Besides, it has been often noted that discrete or continuous inviscid lift and drag adjoint exhibit numerical divergence close to the wall and stagnation streamline for a wide range of subsonic and transonic flow conditions. This is analyzed here using the physical source term perturbation method introduced in reference [Giles and Pierce, AIAA Paper 97-1850, 1997]. With this point of view, the fourth physical source term of appears to be the only one responsible for this behavior. It is also demonstrated that the numerical divergence of the adjoint variables corresponds to the response of the flow to the convected increment of stagnation pressure and diminution of entropy created at the source and the resulting change in lift and drag.
