二维可压缩欧拉流的有限体积离散伴随场分析
Analysis of finite-volume discrete adjoint fields for two-dimensional compressible Euler flows
摘要：
这项工作涉及到与可压缩欧拉方程和经典气动函数有关的离散和连续伴随场的一些问题。离散伴随方程与相应的连续伴随偏微分方程的相容性问题就是其中之一。本文的一个贡献是给出了二维Jameson-Schmidt-Turkel格式在格心有限体积格式中的伴随相容性条件。本文还从一个新的启发式观点出发，通过离散流场和伴随场的连续伴随方程，研究了相容性问题。这两种观点都提供了有用的信息。此外，人们经常注意到，在大范围的亚音速和跨音速流动条件下，离散或连续的无粘升力和阻力伴随项在靠近壁面和滞止流线处表现出数值发散。这里使用参考文献[Giles和Pierce，AIAA Paper 97-1850，1997]中介绍的物理源项扰动方法进行分析。从这个角度来看，第四个物理源项似乎是唯一一个负责这种行为。它还表明，伴随变量的数值发散对应于流动的响应对流的滞止压力的增量和熵的减少在源处创建和由此产生的升力和阻力的变化。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
