基于离散伴随方程求解梯度信息的若干问题研究  

Investigation of gradient computation based on discrete adjoint method

作　　者：黄江涛[1] 刘刚[1] 周铸[1] 高正红[2] 黄勇[1] 

机构地区：[1]中国空气动力研究与发展中心计算空气动力研究所,四川绵阳621000 [2]西北工业大学,陕西西安710072

出　　处：《空气动力学学报》2017年第4期554-562,共9页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(11402288);国家重点研发计划"数值飞行器原型系统"(2016YFB0200704)

摘　　要：基于自主研发的大规模并行化结构化网格RANS求解器PMB3D,开展了黏性离散伴随方程构造、求解方法的研究与讨论。首先对离散伴随求解梯度的思想进行简要介绍,进一步对无黏项、人工黏性项、黏性项部分对离散伴随方程贡献以及变分推导进行了详细介绍;文中对离散伴随方程无黏项、黏性项边界条件实现形式进行了详细研究,并对关键模块变分推导的一些简化方式进行了研究讨论,通过典型宽体飞机标模、外压式超声速进气道算例,分析了所采用的简化处理方式对不同问题梯度求解精度的影响。最后在并行化求解、时间推进以及加速收敛方面进行了探讨、验证。数值模拟表明,文中采用的离散伴随方程形式更有利于程序化、模块化,梯度计算精度完全满足气动优化设计需要。Viscous discrete adjoint equations and the corresponding solving method are studied and discussed based on PMB3D, i. e. , a parallelized in-house CFD code for multi-block structured grid. Firstly, the discrete adjoint gradient strategy is briefly introduced. Secondly, we fully describe the variation derivation and the contribution of inviscid, artificial viscosity, and viscous parts to the discrete adjoint equations. Thirdly, the implementation of the inviscid part and the viscous boundary conditions are studied, and the simplification methods for variation derivation are discussed. Two typical simulations are respectively carried out on a wide-body aircraft and an external compression supersonic inlet to analyze the influences of these simplification methods on the solution precision. Finally, parallel solution, time integration, and convergence acceleration are discussed and validated. Numerical simulation demonstrates that the present discrete adjoint gradient strategy and equations contribute to a convenient programming and modularization. Moreover, the precision of the gradient solution is qualified for aerodynamic optimization design. The present study can be recognized as a useful reference for further study on discrete adjoint method.

关 键 词：离散伴随方程 气动优化 梯度信息 边界条件 时间推进 并行计算 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]