### 定黏假设"对伴随系统求解和梯度精度影响

1. 西北工业大学 动力与能源学院, 西安 710072
• 收稿日期:2021-03-17 修回日期:2021-04-22 发布日期:2021-04-21
• 通讯作者: 王丁喜,E-mail:dingxi_wang@nwpu.edu.cn E-mail:dingxi_wang@nwpu.edu.cn
• 基金资助:
国家科技重大专项(2017-Ⅱ-009-0023);西北工业大学博士论文创新基金(CX2022045)

### Influence of “frozen viscosity assumption” on solution and gradient accuracy of adjoint system

WU Hangkong, WANG Dingxi, HUANG Xiuquan, XU Shenren

1. School of Power and Energy, Northwestern Polytechnical University, Xi'an 710072, China
• Received:2021-03-17 Revised:2021-04-22 Published:2021-04-21
• Supported by:
National Science and Technology Major Project (2017-Ⅱ-009-0023); Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX2022045)

Abstract: The introduction of the "frozen viscosity assumption" can simplify the derivation of the adjoint equation and the differentiation of flow solver subroutines, but can also lead to computational errors of sensitivities and sometimes even solution instability. To investigate the effect of laminar viscosity and eddy viscosity on computational accuracy of sensitivities, this paper presents a study on three different frozen viscosity approaches:the Frozen Laminar Viscosity approach(FLV), Frozen Eddy Viscosity approach(FEV) and Frozen Laminar and Eddy Viscosity approach(FLEV). First, the adjoint equations corresponding to full turbulence and three different frozen viscosity approaches are derived based upon the nonlinear flow equations and the objective function in an algebraic form. Then, we introduce how to use the algorithm differentiation tool to develop the discrete adjoint solver and provide the corresponding flow charts. Finally, the transonic NASA Rotor 67 is used to study the effects of different frozen viscosity approaches on solution stability, sensitivity convergence, sensitivity accuracy and asymptotic convergence rate of residual at different operating points(a peak efficiency point and a near stall point) of the adjoint solver. The results are compared with those of the linear solver and the adjoint solver with full turbulence.