飞行器气动/结构多学科延迟耦合伴随系统数值研究

基于自主研发的大规模并行结构化网格雷诺平均Navier-Stokes（RANS）求解器PMB3D以及流固耦合代码FSC3D建立了飞行器静气动弹性数值模拟技术，进一步基于并行化伴随方程求解器PADJ3D，开展了Navier-Stokes方程与结构动力学方程耦合离散伴随的推导、构造。对各个学科伴随变量进行延迟处理，进行耦合伴随系统的解耦，学科之间的影响通过右端强迫项的形式在方程中体现，通过松耦合形式进行各个学科方程右端项数据传递，各个学科的伴随方程一定程度上能够相对独立，进一步实现了基于LDLT方法的结构伴随方程的高效求解；对典型客机柔性机翼进行梯度信息求解，并与考虑气动弹性影响的差分结果进行对比分析。数值模拟结果表明，延迟耦合伴随形式更有利于保持原有程序结构形式以及程序模块化，梯度计算精度完全满足优化设计需要，能够为柔性机翼飞行器气动/结构多学科优化设计提供研究基础与技术平台。

Numerical study of aero-structural multidisciplinary lagged coupled adjoint system for aircraft

Based on the large-scale parallelized structured grid Reynolds-Averaged Navier-Stokes (RANS)solver PMB3D and the fluid-solid coupling FSC3D, a simulation technology for aircraft aeroelasticity is established. Derivation and construction of the aero-structural coupled adjoint system are carried out by using the parallel adjoint equation solver PADJ3D. The decoupling of the coupled adjoint system is realized by delaying the adjoint variables of each discipline. The influence of various disciplines is represented by the form of the forcing term at the right end of the equation. The cross derivatives of each discipline equation are transferred through a loosely coupled form, the adjoint equations for various disciplines can be solved independently,and the efficient solution of the structure adjoint equation based on LDLT method is further realized. The gradient information of a typical flexible wing of the passenger plane is solved and compared with differential results taking aeroelastic effects into account. The numerical results and the lagged adjoint expression show that the lagged coupling is more conducive to preserving the original program structure and the modularization of the program, the accuracy of the gradient calculation fully meets the requirements of aerodynamic optimization design. The simulation technology proposed can provide research basis and technical support for aero-structural multidisciplinary optimization design of flexible wing.