A discrete adjoint method implemented in a coupled pressure-based RANS solver is presented in this paper. The adjoint equations are solved using an adjoint fixed point iteration that inherits the convergence properties of the primal solver. Automatic differentiation is used extensively for the construction of the adjoint fixed point iteration. The concept of Krylov subspace methods was adopted to stabilize the solution procedure. A common linearization technique in collocated pressure-based algorithms is the introduction of a mass flux variable on the cell faces which is kept constant during the inner iterations. This variable is treated as an independent adjoint variable in related publications. We propose a new method that allows to treat the mass fluxes implicitly in order to take full advantage of the preconditioner of the primal solver. The adjoint solver is general and is not restricted by the commonly used frozen turbulence approximation. It can deal with any turbulence model that is supported by the flow solver as well as any boundary condition. This includes mixing planes and mesh interfaces needed for multi stage turbo machinery simulations. Furthermore, there is no restriction on the choice of objective function. The sensitivities of the adjoint solver have been validated with sensitivities obtained with finite differences.

An entirely surface based interpolation method based on radial basis functions (RBF) was developed to deform the surface mesh. We propose the use of discrete geodesics instead of the classical Euclidean distance as the distance measure for the RBF interpolation. As an alternative, a direct deformation method with adjoint consistent smoothing is also described and used in the presented optimization cases.

The developed adjoint solver and deformation routines were used to optimize a turbulent bend with different Reynolds numbers as well as the the rotor blade of an axial turbine.

本文介绍了一种在基于耦合压力的 RANS 求解器中实现的离散伴随方法。伴随方程使用继承原始求解器收敛特性的伴随不动点迭代求解。自动微分广泛用于构建伴随不动点迭代。采用 Krylov 子空间方法的概念来稳定求解过程。基于压力的并置算法中常见的线性化技术是在单元面上引入质量通量变量，该变量在内部迭代期间保持恒定。该变量在相关出版物中被视为独立的伴随变量。我们提出了一种允许隐式处理质量通量的新方法，以充分利用原始求解器的预处理器。伴随求解器是通用的，不受常用的冻结湍流近似的限制。它可以处理流动求解器支持的任何湍流模型以及任何边界条件。这包括多级涡轮机械仿真所需的混合平面和网格接口。此外，对目标函数的选择没有限制。伴随求解器的灵敏度已经通过有限差分获得的灵敏度进行了验证。对目标函数的选择没有限制。伴随求解器的灵敏度已经通过有限差分获得的灵敏度进行了验证。对目标函数的选择没有限制。伴随求解器的灵敏度已经通过有限差分获得的灵敏度进行了验证。

开发了一种基于径向基函数 (RBF) 的完全基于表面的插值方法来变形表面网格。我们建议使用离散测地线代替经典的欧几里得距离作为 RBF 插值的距离度量。作为替代方案，还描述并在所呈现的优化案例中使用了具有伴随一致平滑的直接变形方法。

开发的伴随求解器和变形例程用于优化具有不同雷诺数的湍流弯曲以及轴流涡轮机的转子叶片。