面向复杂飞行的气动/运动/控制耦合数值虚拟飞行研究综述

邵帅; 梅亚飞; 姚梦玉; 高显忠; 包磊

doi:10.13700/j.bh.1001-5965.2026.0116

面向复杂飞行的气动/运动/控制耦合数值虚拟飞行研究综述

doi: 10.13700/j.bh.1001-5965.2026.0116

国防科技大学试验训练基地，西安 710106

基金项目:

陕西省自然科学基础研究计划一般项目(2024JC-YBQN-0030)；国防科技大学自主创新科学基金项目(25-ZZCX-JDZ-66)；国防科技大学青年自主创新科学基金项目(ZK25-106)

详细信息

通讯作者:
E-mail：shaoshuai_ss@nudt.edu.cn

中图分类号: V211.3
计量
- 文章访问数: 204
- HTML全文浏览量: 61
- PDF下载量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2026-03-02
- 录用日期: 2026-05-08
- 网络出版日期: 2026-06-05
- 整期出版日期: 2026-10-01

A review of numerical virtual flight studies for aerodynamic, motion and control coupling in complex flight conditions

National University of Defense Technology Test Center，Xi’an 710106，China

Funds:

General Program of Shaanxi Provincial Natural Science Basic Research Plan (2024JC-YBQN-0030); Independent Innovation Science Foundation Project of National University of Defense Technology (25-ZZCX-JDZ-66); Youth Independent Innovation Science Foundation Project of National University of Defense Technology (ZK25-106)

More Information

Corresponding author: E-mail：shaoshuai_ss@nudt.edu.cn

摘要

摘要:
数值虚拟飞行(NVF)技术能够高保真地模拟复杂飞行环境下飞行器的动态响应特性，是飞行器控制律设计与飞行品质评估的关键技术。系统综述了气动、运动和控制耦合的NVF技术，重点讨论了该耦合方法在复杂飞行问题中的应用。梳理了NVF的基本框架与技术流程，重点阐述了动网格技术从单一变形向动态混合网格体系的演进历程，及其在保障部件相对运动与计算稳定性中的关键作用，并指出机器学习在网格质量控制中的赋能潜力。针对非定常流场求解，探讨了气动、运动与控制的耦合方式，介绍了从松耦合到紧耦合闭环求解的技术演变，指出紧耦合方法可显著提升对大迎角、过失速等高动态飞行的仿真精度。详细阐述了该耦合方法在高超声速多场耦合、变构飞行、柔性仿生等三大场景中的应用实践。面向未来，在人工智能技术的赋能中，NVF将进一步向高效统一、全系统多场耦合的方向发展，加速飞行器的研制模式向“仿真驱动、数智试验”转型。
- 复杂飞行 /
- 多体分离 /
- 柔性变构型 /
- 多物理场耦合 /
- 非定常流动
Abstract:
High-fidelity simulation of an aircraft’s dynamic reaction characteristics under challenging flight conditions is made possible by numerical virtual flight (NVF) technology, which is essential for designing control laws and assessing flight quality. This paper systematically reviews the NVF technology coupled with aerodynamics, motion, and control, with an emphasis on the application of this coupling method in complex flight problems. This paper outlines the basic framework and technical workflow of NVF, elaborating on the evolution of dynamic mesh technology from single deformation to dynamic hybrid mesh systems, as well as its critical role in ensuring relative motion of components and computational stability, while also pointing out the enabling potential of machine learning in mesh quality control. Regarding unsteady flow field solutions, this paper discusses the coupling modes of aerodynamics, motion, and control, introduces the technical evolution from loose coupling to tightly coupled closed-loop solutions, and highlights that the tightly coupled method can significantly improve the simulation accuracy for high-dynamic flight states such as high angle of attack and post-stall. This paper elaborates on the application practices of this coupling method in three major scenarios: hypersonic multi-field coupling, morphing flight, and flexible bionics. NVF will advance toward effective, unified, and full-system multi-field coupling in the future thanks to artificial intelligence technologies, hastening the shift in aircraft development paradigms toward simulation-driven, digital-intelligent testing.
- complex flight /
- multi-body separation /
- flexible morphing /
- multi-physics coupling /
- unsteady flow

HTML全文

图 1 矩形旋转角度为90°时变形网格质量分布^[29]

Figure 1. Deformation quality distribution of the mesh at a 90° rotation angle of the rectangle^[29]

下载: 全尺寸图片幻灯片

图 2 F6翼身组合体外形和表面网格^[30]

Figure 2. F6 wing-body assembly geometry and surface mesh^[30]

下载: 全尺寸图片幻灯片

图 3 鱼群游动过程中的动态混合网格^[35]

Figure 3. Dynamic mixed mesh for fish school movement^[35]

下载: 全尺寸图片幻灯片

图 4 战斗机外挂物分离投放过程的动态混合网格^[36]

Figure 4. Dynamic hybrid mesh for separation and release process of fighter external stores^[36]

下载: 全尺寸图片幻灯片

图 5 网格自适应算法迭代的整体流程^[59]

Figure 5. Overall process of iterating the grid adaptive algorithm^[59]

下载: 全尺寸图片幻灯片

图 6 松耦合及紧耦合数据交互过程

Figure 6. Loosely coupled and tightly coupled data exchange processes

下载: 全尺寸图片幻灯片

图 7 战斗机非定常机动飞行过程的位置和姿态图^[61]

Figure 7. Position and attitude diagram of fighter aircraft during unsteady maneuver flight^[61]

下载: 全尺寸图片幻灯片

图 8 大后掠角三角翼壁面温度分布^[94]

Figure 8. Temperature distribution on the wing surface of a high-sweep-angle delta wing^[94]

下载: 全尺寸图片幻灯片

图 9 INDI+ESO 控制框架示意图^[99]

Figure 9. INDI+ESO control framework schematic^[99]

下载: 全尺寸图片幻灯片

图 10 复杂扑动规律扑翼飞行器运动仿真^[108]

Figure 10. Dynamic simulation of flapping-wing aircrafts with complex flapping regimes^[108]

下载: 全尺寸图片幻灯片

表 1 不同飞行试验与NVF方法的应用与局限对比

Table 1. Comparison of applications and limitations between different flight tests and NVF methods

方法	应用	局限
风洞试验^[1,9-10]	用于获取典型构型在不同来流工况下的流场结构与气动特性，为气动机理分析和模型验证提供试验依据	工况覆盖有限，难以同时复现高马赫数、大雷诺数、气动力热耦合等极端飞行状态，多体分离与构型快速变化模拟能力受限
虚拟飞行试验^[1,7,11]	在地面风洞试验环境中引入多自由度模型运动控制能力，用于动态响应和控制系统鲁棒性验证	受风洞试验条件限制，对强非线性气动/运动耦合效应、高超声速力热耦合效应复现能力不足，飞行工况全包线覆盖能力不足
数值虚拟飞行-离线耦合阶段^[2-4,10]	基于CFD仿真结果构建气动数据库或代理模型，为飞行仿真提供气动输入	气动、运动与控制数据无法实时反馈，对强非线性、迟滞效应及极端机动场景预测能力有限
数值虚拟飞行-紧耦合阶段^[12-16]	在统一时域内耦合气动、运动与控制系统求解，可用于复杂机动、变构飞行及多场耦合问题的仿真与验证	计算成本高，对动网格质量、时间推进精度与耦合算法稳定性要求严格，工程化应用仍依赖高性能计算支撑

下载: 导出CSV

表 2 NVF中动网格技术的发展历程与演进方向

Table 2. Development history and evolutionary direction of dynamic mesh technology in NVF

时间历程	处理方式	代表方法
20世纪90年代	刚性运动与接口处理	刚性运动网格，滑移网格，多参考系，多块结构网格接口处理
21世纪初期	连续网格变形方法	代数插值类（超限插值、反距离加权），物理类（弹簧法，线性弹性体法，拉普拉斯光顺法），全局插值类（径向基函数、 Delaunay图映射位移传播）
21世纪中后期	重叠/嵌套网格体系	重叠网格，嵌套网格，孔洞切割，供体搜索，守恒插值；背景网格与浸入边界法（笛卡儿网格、切割单元、浸入边界法、自适应网格加密）
21世纪10年代	动态混合网格(工程主流)	变形+局部重构，Delaunay映射，局部拓扑操作（翻转/分裂/合并）近壁面网格质量控制（边界层层状网格保持、各向异性网格保持，网格质量监测与重构触发）
2018年-至今	智能化与多物理场一致网格	智能方法（机器学习网格质量评估、图神经网络网格判别、强化学习驱动自适应网格）；多物理场自适应（h/r/p自适应、流-固-热耦合一致更新、柔性变构型与仿生系统）

下载: 导出CSV

表 3 传统动网格方法与机器学习方法在网格更新中的对比

Table 3. Comparison of traditional dynamic mesh methods and machine learning methods in mesh updates

要素	传统动网格方法	基于机器学习的方法
方法	根据几何关系和物理模型直接计算网格运动	通过已有数据学习网格变化或质量特征
作用对象	网格节点位移、单元变形和局部重构	网格质量、变形趋势或更新策略
稳定性与守恒性	可以明确控制，结果可预测	本身不保证，需要额外约束
应对大变形和多体运动	通过混合变形、重构或重叠网格实现	通过模式识别给出辅助判断
对新工况的适应性	规则固定，但行为稳定	依赖训练数据，需重新训练
当前应用情况	已用于工程问题 NVF 仿真	主要用于标模算例验证

下载: 导出CSV

参考文献(109)

[1]	Fu J Q, Shi Z W, Gong Z, et al. Virtual flight test techniques to predict a blended-wing-body aircraft in-flight departure characteristics[J]. Chinese Journal of Aeronautics, 2022, 35(1): 215-225.
[2]	Salas M D. Digital flight: the last CFD aeronautical grand challenge[J]. Journal of Scientific Computing, 2006, 28(2): 479-505.
[3]	E Q, Yang G W, Li F W. Numerical solution for complete aircraft’s subsonic-transonic-supersonic flow at high angles of attack[J]. Computer Methods in Applied Mechanics and Engineering, 1997, 148(1-2): 11-21.
[4]	Despirito J, Silton S I, Weinacht P. Navier-Stokes predictions of dynamic stability derivatives: evaluation of steady-state methods[J]. Journal of Spacecraft and Rockets, 2009, 46(6): 1142-1154.
[5]	Mi B G, Zhan H, Lu S S. An extended unsteady aerodynamic model at high angles of attack[J]. Aerospace Science and Technology, 2018, 77: 788-801.
[6]	Persova M G, Soloveichik Y G, Belov V K, et al. Modeling of aerodynamic heat flux and thermoelastic behavior of nose caps of hypersonic vehicles[J]. Acta Astronautica, 2017, 136: 312-331.
[7]	Huang M, Wang Z W. A review of wind tunnel based virtual flight testing techniques for evaluation of flight control systems[J]. International Journal of Aerospace Engineering, 2015, 2015(1): 672423.
[8]	陈龙, 伍贻兆, 夏健. CFD/CSD紧耦合及新型动网格方法在气动弹性模拟中的应用[J]. 计算力学学报, 2011, 28(5): 807-812. Chen L, Wu Y Z, Xia J. CFD/CSD closely coupled and new dynamic grid method in application of aeroelastic simulation[J]. Chinese Journal of Computational Mechanics, 2011, 28(5): 807-812(in Chinese).
[9]	Sutrisno, Rohmat T A, Wibowo S B, et al. Vortex dynamics study of the canard deflection angles’ influence on the sukhoi su-30-like model to improve stall delays at high AoA[J]. Aerospace, 2019, 6(2): 12.
[10]	Thibert J J, Arnal D. A review of ONERA aerodynamic research in support of a future supersonic transport aircraft[J]. Progress in Aerospace Sciences, 2000, 36(8): 581-627.
[11]	Lee D K, Han J H. Safety-guaranteed flight test environment for micro air vehicles[J]. AIAA Journal, 2015, 54(3): 1018-1029.
[12]	Schütte A, Einarsson G, Raichle A, et al. Numerical simulation of maneuvering aircraft by aerodynamic, flight mechanics and structural mechanics coupling[J]. Journal of Aircraft, 2009, 46(1): 53-64.
[13]	杨云军, 周伟江, 崔尔杰. 耦合时间精度对模拟飞行器自由运动特性的影响[J]. 计算物理, 2007, 24(1): 42-48. Yang Y J, Zhou W J, Cui E J. Influence of coupling time accuracy on the simulation of aircraft free movement[J]. Chinese Journal of Computational Physics, 2007, 24(1): 42-48(in Chinese).
[14]	Guo Z Z, Dai G, Yang H, et al. Unsteady flow simulation of a variable-sweep morphing aircraft coupled with flight control system[J]. International Journal of Modern Physics B, 2020, 34(14-16): 2040073.
[15]	Liang Y M, Li G N, Xu M, et al. An intelligent control method based on artificial neural network for numerical flight simulation of the basic finner projectile with pitching maneuver[J]. Defence Technology, 2024, 32: 663-674.
[16]	Wang N H, Ma R, Chang X H, et al. Numerical virtual flight simulation of quasi-cobra maneuver of a fighter aircraft[J]. Journal of Aircraft, 2020, 58(1): 138-152.
[17]	张来平, 段旭鹏, 常兴华, 等. 基于Delaunay背景网格插值和局部网格重构的变形体动态混合网格生成技术[J]. 空气动力学学报, 2009, 27(1): 32-40. Zhang L P, Duan X P, Chang X H, et al. A hybrid dynamic grid generation technique for morphing bodies based on Delaunay graph and local remeshing[J]. Acta Aerodynamica Sinica, 2009, 27(1): 32-40(in Chinese).
[18]	张来平, 邓小刚, 张涵信. 动网格生成技术及非定常计算方法进展综述[J]. 力学进展, 2010, 40(4): 424-447. Zhang L P, Deng X G, Zhang H X. Reviews of moving grid generation techniques and numerical methods for unsteady flow[J]. Advances in Mechanics, 2010, 40(4): 424-447(in Chinese).
[19]	Liu X Q, Qin N, Xia H. Fast dynamic grid deformation based on Delaunay graph mapping[J]. Journal of Computational Physics, 2006, 211(2): 405-423.
[20]	Chaderjian N M, Schiff L B. Numerical simulation of forced and free-to-roll delta-wing motions[J]. Journal of Aircraft, 1996, 33(1): 93-99.
[21]	Woods B K S, Dayyani I, Friswell M I. Fluid/structure-interaction analysis of the fish-bone-active-camber morphing concept[J]. Journal of Aircraft, 2015, 52(1): 307-319.
[22]	Ouyang Y, Gu Y S, Kou X P, et al. Active flutter suppression of wing with morphing flap[J]. Aerospace Science and Technology, 2021, 110: 106457.
[23]	Fonzi N, Brunton S L, Fasel U. Data-driven nonlinear aeroelastic models of morphing wings for control[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020, 476(2239): 20200079.
[24]	Yuan W X, Sandhu R, Poirel D. Fully coupled aeroelastic analyses of wing flutter towards application to complex aircraft configurations[J]. Journal of Aerospace Engineering, 2021, 34(2): 04020117.
[25]	张来平, 马戎, 常兴华, 等. 虚拟飞行中气动、运动和控制耦合的数值模拟技术[J]. 力学进展, 2014, 44(1): 376-417. Zhang L P, Ma R, Chang X H, et al. Review of aerodynamics/kinematics/flight-control coupling methods in virtual flight simulations[J]. Advances in Mechanics, 2014, 44(1): 376-417(in Chinese).
[26]	谭伟伟, 刘峰博, 张一帆. 基于线性弹性体的网格变形方法研究[J]. 航空计算技术, 2017, 47(2): 37-40. Tan W W, Liu F B, Zhang Y F. Study on linear elastic solid based grid deformation method[J]. Aeronautical Computing Technique, 2017, 47(2): 37-40(in Chinese).
[27]	张兵, 韩景龙. 带旋转修正的弹簧-TFI混合动网格方法[J]. 航空学报, 2011, 32(10): 1815-1823. Zhang B, Han J L. Spring-TFI hybrid dynamic mesh method with rotation correction[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(10): 1815-1823(in Chinese).
[28]	张伟伟, 高传强, 叶正寅. 气动弹性计算中网格变形方法研究进展[J]. 航空学报, 2014, 35(2): 303-319. Zhang W W, Gao C Q, Ye Z Y. Research progress on mesh deformation method in computational aeroelasticity[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(2): 303-319(in Chinese).
[29]	孙岩, 邓小刚, 王光学, 等. 基于径向基函数改进的Delaunay图映射动网格方法[J]. 航空学报, 2014, 35(3): 727-735. Sun Y, Deng X G, Wang G X, et al. Improvement on delaunay graph mapping dynamic grid method based on radial basis functions[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3): 727-735(in Chinese).
[30]	孙岩, 邓小刚, 王运涛, 等. RBFTFI结构动网格技术在风洞静气动弹性修正中的应用[J]. 工程力学, 2014, 31(10): 228-233. Sun Y, Deng X G, Wang Y T, et al. Application of structural dynamic grid method based on RBFTFI on wind tunnel static aero-elastic modification[J]. Engineering Mechanics, 2014, 31(10): 228-233(in Chinese).
[31]	Wang Z J, Parthasarathy V. A fully automated Chimera methodology for multiple moving body problems[J]. International Journal for Numerical Methods in Fluids, 2000, 33(7): 919-938.
[32]	Nakahashi K, Togashi F, Sharov D. Intergrid-boundary definition method for overset unstructured grid approach[J]. AIAA Journal, 2000, 38(11): 2077-2084.
[33]	段旭鹏, 常兴华, 张来平. 基于动态混合网格的多体分离数值模拟方法[J]. 空气动力学学报, 2011, 29(4): 447-452. Duan X P, Chang X H, Zhang L P. A CFD-and-6DOF-coupled solver for multiple moving object problems based on dynamic hybrid grids[J]. Acta Aerodynamica Sinica, 2011, 29(4): 447-452(in Chinese).
[34]	Gillebaart T, Blom D S, Van Zuijlen A H, et al. Adaptive radial basis function mesh deformation using data reduction[J]. Journal of Computational Physics, 2016, 321: 997-1025.
[35]	常兴华, 王年华, 马戎, 等. 并行重叠/变形混合网格生成技术及其应用[J]. 气体物理, 2019, 4(6): 12-21. Chang X H, Wang N H, Ma R, et al. Dynamic hybrid mesh generator coupled with overset and deformation in parallel environment[J]. Physics of Gases, 2019, 4(6): 12-21(in Chinese).
[36]	陈坚强. 国家数值风洞(NNW)工程关键技术研究进展[J]. 中国科学(技术科学), 2021, 51(11): 1326-1347. Chen J Q. Advances in the key technologies of Chinese national numerical windtunnel project[J]. Scientia Sinica (Technologica), 2021, 51(11): 1326-1347(in Chinese).
[37]	李海峰, 吴冀川, 刘建波, 等. 有限元网格剖分与网格质量判定指标[J]. 中国机械工程, 2012, 23(3): 368-377. Li H F, Wu J C, Liu J B, et al. Finite element mesh generation and decision criteria of mesh quality[J]. China Mechanical Engineering, 2012, 23(3): 368-377(in Chinese).
[38]	Sorgente T, Biasotti S, Manzini G, et al. A survey of indicators for mesh quality assessment[J]. Computer Graphics Forum, 2023, 42(2): 461-483.
[39]	Secco N R, Kenway G K W, He P, et al. Efficient mesh generation and deformation for aerodynamic shape optimization[J]. AIAA Journal, 2021, 59(4): 1151-1168.
[40]	李绍磊, 郑建靖, 尚萌萌. 基于非结构网格的飞行器多体分离数值模拟[J]. 计算机应用, 2016, 36(6): 1741-1744. Li S L, Zheng J J, Shang M M. Numerical simulation of flight vehicle multi-body separation based on unstructured mesh[J]. Journal of Computer Applications, 2016, 36(6): 1741-1744(in Chinese).
[41]	杨宇辰. 可压缩流动模拟的自适应网格方法研究[D]. 南京: 南京航空航天大学, 2023. Yang Y C. Research on adaptive mesh method for compressible flow simulation[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2023(in Chinese).
[42]	Haubner J, Hellan O, Zeinhofer M, et al. Learning mesh motion techniques with application to fluid-structure interaction[J]. Computer Methods in Applied Mechanics and Engineering, 2024, 424: 116890.
[43]	刘翰林, 崔会敏, 张珍, 等. 基于BP算法的二维阵面推进网格划分方法的优化与应用[J]. 计算力学学报, 2024, 41(4): 626-633. Liu H L, Cui H M, Zhang Z, et al. Optimization and application of two-dimensional advancing grid generation method based on BP algorithm[J]. Chinese Journal of Computational Mechanics, 2024, 41(4): 626-633(in Chinese).
[44]	Wang Z C, Chen X H, Li T J, et al. Evaluating mesh quality with graph neural networks[J]. Engineering with Computers, 2022, 38(5): 4663-4673.
[45]	Foucart C, Charous A, Lermusiaux P F J. Deep reinforcement learning for adaptive mesh refinement[J]. Journal of Computational Physics, 2023, 491: 112381.
[46]	万嘉伟. 龙格-库塔法数值求解基于有限体积的不可压Navier-Stokes方程和流固耦合问题[D]. 成都: 西南交通大学, 2020. Wan J W. The numerical solution of finite-volume based incompressible navier-stokes equations and fluid-structure interaction problems by Runge-Kutta methods[D]. Chengdu: Southwest Jiaotong University, 2020(in Chinese).
[47]	张乐, 章定国. 基于向后差分法求解多体系统动力学微分-代数方程组的双循环隐式积分方法[J]. 机械工程学报, 2016, 52(7): 79-87. Zhang L, Zhang D G. Two-loop implicit integration method based on backward differential formulation for differential-algebraic equations of multibody system dynamics[J]. Journal of Mechanical Engineering, 2016, 52(7): 79-87(in Chinese).
[48]	贡伊明, 张伟伟, 刘溢浪. 非定常求解的内迭代初值对计算效率的影响研究[J]. 西北工业大学学报, 2016, 34(1): 11-17. Gong Y M, Zhang W W, Liu Y L. Researching how initial value of internal iteration impacts on computational efficiency in unsteady flow solving[J]. Journal of Northwestern Polytechnical University, 2016, 34(1): 11-17(in Chinese).
[49]	马晓永, 艾俊强, 宋笔锋. 有限差分法在机翼气动外形优化仿真中的应用[C]//第14届中国系统仿真技术及其应用学术年会论文集. 武汉: 科研出版社, 2012: 214-218. Ma X Y, Ai J Q, Song B F. Application of finite difference method in wing aerodynamic shape optimization simulation[C]//Proceedings of the 14th China Annual Conference on System Simulation Technology and Its Application. Wuhan: Scientific Research Publishing Inc. , 2012: 214-218(in Chinese).
[50]	Abalakin I, Dervieux A, Kozubskaya T. High accuracy finite volume method for solving nonlinear aeroacoustics problems on unstructured meshes[J]. Chinese Journal of Aeronautics, 2006, 19(2): 97-104.
[51]	席柯, 阎超, 黄宇. 带反馈控制的基本带翼外形的耦合气动/运动数值模拟研究[J]. 空气动力学学报, 2016, 34(2): 182-189. Xi K, Yan C, Huang Y. Coupled CFD/RBD modelingfor a basic finner projectile with control[J]. Acta Aerodynamica Sinica, 2016, 34(2): 182-189(in Chinese).
[52]	李少伟, 张元静, 周丹杰. 支撑约束的并联飞行器多体分离安全性数值研究[C]//第九届全国流体力学学术会议论文集. 北京: 中国力学学会, 2016: 376. Li S W, Zhang Y J, Zhou D J. Numerical study on the safety of multi-body separation of parallel aircraft with support constraints[C]//Proceedings of the 9th National Conference on Fluid Mechanics. Beijing: The Chinese Society of Theoretical and Applied Mechanics, 2016: 376(in Chinese).
[53]	Deng Y, Jiao Z X, Xu Y Z. Frequency-domain analysis of fluid-structure interaction in aircraft hydraulic pipeline systems: numerical and experimental studies[J]. Journal of Zhejiang University-Science A (Applied Physics & Engineering), 2024, 25(8): 605-618.
[54]	白玉柔, 王永锋, 马艳红, 等. 大涵道比风扇转子双套齿连接稳健性及其力学影响[J]. 航空动力学报, 2025, 40(7): 20240124. Bai Y R, Wang Y F, Ma Y H, et al. Robustness and mechanical effects of double set tooth connection for large bypass ratio fan rotor[J]. Journal of Aerospace Power, 2025, 40(7): 20240124(in Chinese).
[55]	黄国. 高超声速环境下缝隙热环境的数值模拟研究[D]. 北京: 北京交通大学, 2017. Huang G. Numerical simulation for heating environment of gap in hypersonic flow[D]. Beijing: Beijing Jiaotong University, 2017(in Chinese).
[56]	于要杰, 刘锋, 高超, 等. 一种基于块雅可比迭代的高阶FR格式隐式方法[J]. 力学学报, 2021(6): 1586-1598. Yu Y J, Liu F, Gao C, et al. An implicit block jacobi approach for high-order flux reconstruction method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021(6): 1586-1598(in Chinese).
[57]	孙岩. 共轴刚性旋翼直升机流场和噪声高精度模拟及质量射流控制研究[D]. 南京: 南京航空航天大学, 2022. Sun Y. High-accuracy simulation of flowfield, noise and TAMI control for rigid coaxial rotor helicopter[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2022(in Chinese).
[58]	郭曼丽, 王园丁, 谭俊杰, 等. N-S方程耦合雷诺平均湍流模型无网格算法研究[J]. 南京理工大学学报(自然科学版), 2019, 43(5): 548-555. Guo M L, Wang Y D, Tan J J, et al. Meshless method coupled with different Reynolds average turbulence model for solving Navier-Stokes equation[J]. Journal of Nanjing University of Science and Technology, 2019, 43(5): 548-555(in Chinese).
[59]	李彩云, 安慰, 刘学军, 等. 基于机器学习的非定常流场网格自适应[J]. 空气动力学学报, 2023, 41(6): 89-101. Li C Y, An W, Liu X J, et al. Mesh adaptation for unsteady flow field based on machine learning[J]. Acta Aerodynamica Sinica, 2023, 41(6): 89-101(in Chinese).
[60]	赵明, 丁秋实, 曹京硕, 等. 基于间断伽辽金方法的波形前缘动态失速流场仿真分析[C]//第十二届全国流体力学学术会议论文集. 北京: 中国力学学会, 2022: 865. Zhao M, Ding Q S, Cao J S, et al. Simulation analysis of dynamic stall flow field on wavy leading edge based on discontinuous Galerkin method[C]//Proceedings of the 12th National Conference on Fluid Mechanics. Beijing: The Chinese Society of Theoretical and Applied Mechanics, 2022: 865(in Chinese).
[61]	Yan L, Chang X H, Wang N H, et al. Numerical virtual flight investigation for longitudinal maneuver of a generic fighter based on machine learning[J]. Physics of Fluids, 2024, 36(7): 077131.
[62]	刘艳, 白俊强, 华俊, 等. 基于RBF插值技术的CFD/CSD非线性耦合分析方法研究[J]. 计算力学学报, 2014, 31(1): 120-127. Liu Y, Bai J Q, Hua J, et al. A approach to CFD/CSD non-linear coupling based on RBF interpolation technology[J]. Chinese Journal of Computational Mechanics, 2014, 31(1): 120-127(in Chinese).
[63]	达兴亚, 陶洋, 赵忠良. 基于预估校正和嵌套网格的虚拟飞行数值模拟[J]. 航空学报, 2012, 33(6): 977-983. Da X Y, Tao Y, Zhao Z L. Numerical simulation of virtual flight based on predictioncorrection coupling method and chimera grid[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(6): 977-983(in Chinese).
[64]	马戎, 常兴华, 赫新, 等. 流动/运动松耦合与紧耦合计算方法及稳定性分析[J]. 气体物理, 2016, 1(6): 36-49. Ma R, Chang X H, He X, et al. Loose and strong coupling methods for flow/kinematics coupled simulations and stability analysis[J]. Physics of Gases, 2016, 1(6): 36-49(in Chinese).
[65]	王博, 刘勇. 新型无铰式旋翼气弹综合分析的全本征方程方法[J]. 南京航空航天大学学报, 2016, 48(2): 261-267. Wang B, Liu Y. Comprehensive aeroelasticity analysis on new hingeless rotor using fully intrinsic equations[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2016, 48(2): 261-267(in Chinese).
[66]	李怀璐, 王旭, 王霄, 等. 大迎角机动飞行的气动力建模与飞行仿真[J]. 航空学报, 2023, 44(19): 78-95. Li H L, Wang X, Wang X, et al. Aerodynamic modeling and flight simulation of maneuver flight at high angle of attack[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 78-95(in Chinese).
[67]	王建华, 刘鲁华, 王鹏, 等. 高超声速飞行器俯冲段制导控制一体化设计方法[J]. 航空学报, 2017, 38(3): 320328. Wang J H, Liu L H, Wang P, et al. Integrated guidance and control scheme for hypersonic vehicles in dive phase[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(3): 320328(in Chinese).
[68]	Gong Q W, Li Z D, He R Y, et al. Numerical study of flexible wing aerodynamic characteristics of bionic flapping-wing vehicle in Martian atmosphere[J]. Journal of Physics: Conference Series, 2025, 3078(1): 012001.
[69]	Guide. Guide for the verification and validation of computational fluid dynamics simulations[M]. Reston: AIAA, 1998.
[70]	赵忠良, 吴军强, 李浩, 等. 2.4 m跨声速风洞虚拟飞行试验技术研究[J]. 航空学报, 2016, 37(2): 504-512. Zhao Z L, Wu J Q, Li H, et al. Investigation of virtual flight testing technique based on 2.4 m transonic wind tunnel[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(2): 504-512(in Chinese).
[71]	赵炜, 陈江涛, 肖维, 等. 国家数值风洞(NNW)验证与确认系统关键技术研究进展[J]. 空气动力学学报, 2020, 38(6): 1165-1172. Zhao W, Chen J T, Xiao W, et al. Advances in the key technologies of verification and validation system of national numerical windtunnel project[J]. Acta Aerodynamica Sinica, 2020, 38(6): 1165-1172(in Chinese).
[72]	Babuska I, Oden J T. Verification and validation in computational engineering and science: basic concepts[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(36-38): 4057-4066.
[73]	Celik I B, Ghia U, Roache P J, et al. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications[J]. Journal of Fluids Engineering, 2008, 130(7): 078001.
[74]	Calhoun D, Leveque R J. An accuracy study of mesh refinement on mapped grids[C]//Adaptive Mesh Refinement-Theory and Applications. Berlin: Springer, 2006: 91-101.
[75]	Roy C J. Review of code and solution verification procedures for computational simulation[J]. Journal of Computational Physics, 2005, 205(1): 131-156.
[76]	周毓麟, 李德元. 非定常流体力学数值方法的若干问题[J]. 数学进展, 1981, 10(1): 48-56. Zhou Y L, Li D Y. Some problems of numerical methods of unsteady fluid mechanics[J]. Advances in Mathematics, 1981, 10(1): 48-56(in Chinese).
[77]	高智. 数值摄动算法及其CFD格式[J]. 力学进展, 2010, 40(6): 607-633. Gao Z. Numerical perturbation algorithm and its CFD schemes[J]. Advances in Mechanics, 2010, 40(6): 607-633(in Chinese).
[78]	郭林亮, 祝明红, 孔鹏, 等. 风洞虚拟飞行模型机与原型机动力学特性分析[J]. 航空学报, 2016, 37(8): 2583-2593. Guo L L, Zhu M H, Kong P, et al. Analysis of dynamic characteristics between prototype aircraft and scaled-model of virtual flight test in wind tunnel[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(8): 2583-2593(in Chinese).
[79]	Da Ronch A, Panzeri M, Drofelnik J, et al. Sensitivity and calibration of turbulence model in the presence of epistemic uncertainties[J]. CEAS Aeronautical Journal, 2020, 11(1): 33-47.
[80]	宁小磊. 数字化试验仿真模型验证方法验证分辨率研究[J]. 西北工业大学学报, 2025, 43(4): 831-842. Ning X L. Study on validation resolution of digitized test simulation model validation method[J]. Journal of Northwestern Polytechnical University, 2025, 43(4): 831-842(in Chinese).
[81]	Eça L, Vaz G, Hoekstra M, et al. Assessment of discretization uncertainty estimators based on grid refinement studies[J]. Journal of Verification, Validation and Uncertainty Quantification, 2021, 6(4): 041006.
[82]	张斌, 杨涛, 丰志伟, 等. 网格质量反馈的弹性体动网格改进[J]. 国防科技大学学报, 2018, 40(1): 10-16. Zhang B, Yang T, Feng Z W, et al. Improvement of elasticity-based dynamic grid method based on mesh quality feedback[J]. Journal of National University of Defense Technology, 2018, 40(1): 10-16(in Chinese).
[83]	Hao J X, Wang Q. A class of finite difference schemes with adaptive controllable dispersion and low dissipation for compressible turbulence[J]. Fluids, 2025, 10(2): 43.
[84]	Liang T, Shyy W, Fu L. Efficient arbitrary-high-order TENO schemes with local adaptive dissipation for compressible flow simulation on unstructured meshes[J]. Journal of Scientific Computing, 2025, 104(1): 1.
[85]	Wang D D, Du Y M, Jin Y, et al. Comparative study on predicting turbulent kinetic energy budget using high-order upwind scheme and non-dissipative central scheme[J]. Advances in Aerodynamics, 2024, 6(1): 24.
[86]	吴惠松, 林麒, 柳汀, 等. 风洞虚拟飞行试验模型绳系并联支撑机构[J]. 航空学报, 2022, 43(8): 308-320. Wu H S, Lin Q, Liu T, et al. Wire-driven parallel suspension mechanism of virtual flight test model in wind tunnel[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(8): 308-320(in Chinese).
[87]	林麒, 何聪, 林北辰, 等. 用于旋成体飞行器模型风洞虚拟飞行试验的支撑装置和试验系统: CN114778064B[P]. 2024-06-04. Lin Q, He C, Lin B C, et al.Support device and test system for wind tunnel virtual flight test of axisymmetric aircraft model: CN114778064B[P]. 2024-06-04(in Chinese).
[88]	杜洪亮, 张伟. 冰风洞虚拟仪器环境参数测试系统设计实现[J]. 测控技术, 2016, 35(3): 8-12. Du H L, Zhang W. Design and realization of virtual instrument environment parameters measurement system for ice wind tunnel[J]. Measurement & Control Technology, 2016, 35(3): 8-12(in Chinese).
[89]	Shin E Y, Howland M F. Accelerated Bayesian calibration and uncertainty quantification of RANS turbulence model parameters for stratified atmospheric boundary layer flows[J]. Boundary-Layer Meteorology, 2025, 192(1): 3.
[90]	Xue Y L, Feng Y L, Zheng X J. Uncertainty quantification of compressibility corrections on SA turbulence model for high Mach number flows[J]. Aerospace Science and Technology, 2025, 162: 110184.
[91]	贾洲侠, 吴振强, 吴建国, 等. 飞行器气动热与结构传热双向耦合研究[J]. 强度与环境, 2019, 46(6): 16-23. Jia Z X, Wu Z Q, Wu J G, et al. Study on two-way coupled fluid-structure-thermal analysis for hypersonic vehicles[J]. Structure & Environment Engineering, 2019, 46(6): 16-23(in Chinese).
[92]	Wu J, Zhang Z, Hou A P, et al. Thermal aeroelastic characteristics of inflatable reentry vehicle experiment (IRVE) in hypersonic flow[J]. International Journal of Aerospace Engineering, 2021, 2021(1): 6673818.
[93]	Bai Y G, Cao L X, Xu X L, et al. Thermal-aero-elastic analysis of a typical all-moving control surface[J]. Thermal Science and Engineering Progress, 2022, 31: 101297.
[94]	Wang W J, Qian W, Bai Y G, et al. Numerical studies on the thermal-fluid-structure coupling analysis method of hypersonic flight vehicle[J]. Thermal Science and Engineering Progress, 2023, 40: 101792.
[95]	Guo T Q, Shen E N, Lu Z L, et al. Thermal flutter prediction at trajectory points of a hypersonic vehicle based on aerothermal synchronization algorithm[J]. Aerospace Science and Technology, 2019, 94: 105381.
[96]	王晓鹏. 导弹弹射发射分离轨迹的数值研究[J]. 弹箭与制导学报, 2012, 32(3): 69-72. Wang X P. The numerical investigation on separation track of missile ejected from aircraft[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2012, 32(3): 69-72(in Chinese).
[97]	李孝伟, 范绪箕. 基于动态嵌套网格的飞行器外挂物投放的数值模拟[J]. 空气动力学学报, 2004(1): 114-117. Li X W, Fan X J. Simulation of the release of store based on the moving chimera grid technique[J]. Acta Aerodynamica Sinica, 2004(1): 114-117(in Chinese).
[98]	安效民, 高昕, 屈佑文, 等. 变后掠翼的气动弹性特性分析[J]. 力学学报, 2025, 57(12): 3019-3031. An X M, Gao X, Qu Y W, et al. Analysis of aeroelastic characteristics of a variable-sweep wing[J]. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(12): 3019-3031(in Chinese).
[99]	刘昊东, 杨建东, 赵文文, 等. 变构型飞行器增量非线性动态逆姿态控制律设计[J]. 战术导弹技术, 2024(4): 83-91. Liu H D, Yang J D, Zhao W W, et al. Incremental nonlinear dynamic inversion attitude control law design for morphing aircraft[J]. Tactical Missile Technology, 2024(4): 83-91(in Chinese).
[100]	李墨吟, 马泽远, 周建平, 等. 基于神经网络的变后掠翼飞行器自适应控制方法研究[J]. 弹箭与制导学报, 2021, 41(5): 73-77. Li M Y, Ma Z Y, Zhou J P, et al. Research on adaptive control method of variable-sweep wing aircraft based on neural network[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2021, 41(5): 73-77(in Chinese).
[101]	Li C X, Wu H N. A dynamic neural network-based control method using reinforcement learning for nonlinear parameter-varying system with application to morphing aircraft[J]. IEEE Transactions on Neural Networks and Learning Systems, 2025, 99: 1-13.
[102]	Cheng X M, Wang Y X, Zhao J, et al. Data-driven adaptive hybrid-based control for some tiltrotor UAVs in the low-speed flight[J]. Aerospace Science and Technology, 2026, 170: 111513.
[103]	Yu J S, Yu J J. Neural learning control of fighter aircraft at high-angle-of-attack maneuvers with online recorded data and disturbance observer[J]. IEEE Access, 2026, 14: 39702-39712.
[104]	Deng S H, Xiao T H, VAN Oudheusden B, et al. A dynamic mesh strategy applied to the simulation of flapping wings[J]. International Journal for Numerical Methods in Engineering, 2016, 106(8): 664-680.
[105]	Addo-Akoto R, Han J S, Han J H. Roles of wing flexibility and kinematics in flapping wing aerodynamics[J]. Journal of Fluids and Structures, 2021, 104: 103317.
[106]	Li G, Law Y Z, Jaiman R K. A novel 3D variational aeroelastic framework for flexible multibody dynamics: application to bat-like flapping dynamics[J]. Computers & Fluids, 2019, 180: 96-116.
[107]	Xue Y J, Cai X F, Xu R, et al. Wing kinematics-based flight control strategy in insect-inspired flight systems: deep reinforcement learning gives solutions and inspires controller design in flapping MAVs[J]. Biomimetics, 2023, 8(3): 295.
[108]	Chen A, Song B F, Liu K, et al. Flapping-wing robot achieves bird-style self-takeoff by adopting reconfigurable mechanisms[J]. Science Advances, 2025, 11(36): eadx0465.
[109]	刘笑尘, 何心怡, 何国毅, 等. 蜻蜓非均匀柔性前翼扑动飞行的气动性能研究[J]. 力学学报, 2022, 54(4): 991-1003. Liu X C, He X Y, He G Y, et al. The aerodynamic performance of non-uniform flexible dragonfly’s forewing in flapping flight[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(4): 991-1003(in Chinese).