矢量喷管非定常流场计算与动态数学模型研究
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摘要
推力矢量技术是现代战机具有敏捷性、过失速机动能力、良好的飞行品质的关键技术，其已成为第四代战斗机的必备技术和第三代战斗机改型的热门技术，得到了越来越多的重视。矢量喷管是实现推力矢量的关键部件，建立其数学模型是推力矢量技术尤其是开展带矢量喷管的发动机研究以及飞／推一体化综合控制研究的基础，具有十分重要的意义。
本文的研究就是针对矢量喷管数学模型的建立开展的。由于气流在喷管流动中具有复杂的三维非定常的特征，因此，建立其动态数学模型有着更为重要的工程及理论价值。本文通过CFD计算获得矢量喷管的性能参数，如流量系数、推力系数以及有效推力矢量角等与矢量喷管压比、面积比以及几何偏转角之间的关系数据，并利用函数逼近理论建立了矢量喷管的动态数学模型。本文的主要工作和贡献如下：
1．研究了Jamson提出了中心型有限体积法，并改进了其在边界上的处理，通过验证计算验证了本文发展的矢量喷管三维有粘流动计算程序的正确性。
2．利用该程序计算了某矢量喷管在不同的压比、面积比和几何偏转角下的200多种三维有粘流场，获得了矢量喷管的性能数据。
3．研究了影响矢量喷管性能的因素，研究了压比、面积比以及几何偏角对矢量喷管性能的影响。
4．研究了喷管流动分离现象和流动分离对喷管性能的影响，以及导致分离流动的宏观因素。
5．研究了矢量喷管动态偏转过程中气流的非定常流动和矢量喷管非定常流动计算方法，计算了矢量喷管在发动机某中间状态和加力状态下的非定常流场。
6．分析比较了定常流动计算结果和非定常流动计算结果，得出了定常流动计算结果和非定常计算结果的基本一致性，从而为工程通过定常计算或试验来研究矢量喷管以及建立其数学模型提供了依据。
7．研究了基于矢通量分裂的高分辨率迎风型有限体积法，重点研究了
Sieger Warming、Vn Leer、Roe以及 AUSM”分裂格式。
8．研究了B样条参数拟合方法，提出了三元B样条参数拟合方法。以此
为基础，建立了轴对称矢量喷管的三自由参数动态数学模型。
Thrust Vectoring is the key technique for the modem fighter with agility and post-stall maneuver ability and good flight quality. And now it is the necessary technique for the fourth generation fighter and hot technique for the performance improvement for the third generation fighter. Therefore, more and more attention is paid to this technique recently. Vectoring nozzle is the main component for generating vectoring thrust. And establishing the model of the thrust vectoring nozzle is the base for researching thrust vectoring technique and engine performance with vectoring nozzle, especially the integration of flight and propulsion system control (IFPSC). So thrust vector modeling is very important and meaningful.
This paper is focused on how to establish mathematical model of vectoring nozzle on the basis of flow field calculation. In order to obtain transient mathematical model as vectoring deflection which is very important in engineering and valuable in theory, three-dimensional and unsteady flow fields must be researched. In our study computational fluid dynamic(CFD) is used to calculate the performance parameters such as the coefficients of mass rate and thrust and efficient deflected angle of the thrust vectoring nozzle. CFD is also used to get the data of performance parameters of the nozzle at different nozzle pressure ratio, different nozzle area ratio and different geometric defected angle. The theory of function approximation is used to establish the transient model of thrust vectoring with the data calculated. The main works and contribution of this paper are as follows:
1.Central type finite volume method proposed by Jameson A. is investigated and the boundary condition of the method is improved. Compared with the testing data it is proved that the program for 3D viscosity steady flow in thrust vectoring nozzle developed is correct and reasonable.
2. More than 200 different condition 3D viscosity steady flow fields in the thrust vectoring nozzle at different nozzle pressure ratio and different nozzle area
ratio and different geometric defected angle is calculated by the program developed. And the related performance parameters are acquired by numerical simulation.
3. The affecting factors of the performance parameters of the thrust vectoring nozzle are investigated. And the affect of nozzle pressure ratio, nozzle area ratio and geometric defected angle on the performance parameters is also investigated.
4. The affect of flow separation on the nozzle is investigated and the macroscopical factor that leads to flow separation is also analyzed.
5. The unsteady flow as thrust vectoring nozzle deflecting dynamically is investigated. The method of calculating the unsteady flow in the nozzle is given and the flow of the nozzle in the maximum power setting and maximum A/B power setting of the engine is calculated.
6. The calculating results of steady flow and unsteady flow in the nozzle are compared. And it proves that both the results of the steady flow and the results of the unsteady .flow are uniform basically. This is very valuable because it is convenient to study the flow in the vectoring nozzle by steady hypothesis or steady test.
7. The upwind finite volume method based on flux vector splitting is investigated, especially the splitting scheme of Steger-Warming, Van Leer, Roe and AUSM+.
8.The method of the parameter fitting based B-spline is investigated. And the method of the parameter fitting which has three free variables is proposed. Based on this method the transient mathematical model of the thrust vectoring nozzle which has three free variables is established.
本文的研究就是针对矢量喷管数学模型的建立开展的。由于气流在喷管流动中具有复杂的三维非定常的特征，因此，建立其动态数学模型有着更为重要的工程及理论价值。本文通过CFD计算获得矢量喷管的性能参数，如流量系数、推力系数以及有效推力矢量角等与矢量喷管压比、面积比以及几何偏转角之间的关系数据，并利用函数逼近理论建立了矢量喷管的动态数学模型。本文的主要工作和贡献如下：
1．研究了Jamson提出了中心型有限体积法，并改进了其在边界上的处理，通过验证计算验证了本文发展的矢量喷管三维有粘流动计算程序的正确性。
2．利用该程序计算了某矢量喷管在不同的压比、面积比和几何偏转角下的200多种三维有粘流场，获得了矢量喷管的性能数据。
3．研究了影响矢量喷管性能的因素，研究了压比、面积比以及几何偏角对矢量喷管性能的影响。
4．研究了喷管流动分离现象和流动分离对喷管性能的影响，以及导致分离流动的宏观因素。
5．研究了矢量喷管动态偏转过程中气流的非定常流动和矢量喷管非定常流动计算方法，计算了矢量喷管在发动机某中间状态和加力状态下的非定常流场。
6．分析比较了定常流动计算结果和非定常流动计算结果，得出了定常流动计算结果和非定常计算结果的基本一致性，从而为工程通过定常计算或试验来研究矢量喷管以及建立其数学模型提供了依据。
7．研究了基于矢通量分裂的高分辨率迎风型有限体积法，重点研究了
Sieger Warming、Vn Leer、Roe以及 AUSM”分裂格式。
8．研究了B样条参数拟合方法，提出了三元B样条参数拟合方法。以此
为基础，建立了轴对称矢量喷管的三自由参数动态数学模型。
Thrust Vectoring is the key technique for the modem fighter with agility and post-stall maneuver ability and good flight quality. And now it is the necessary technique for the fourth generation fighter and hot technique for the performance improvement for the third generation fighter. Therefore, more and more attention is paid to this technique recently. Vectoring nozzle is the main component for generating vectoring thrust. And establishing the model of the thrust vectoring nozzle is the base for researching thrust vectoring technique and engine performance with vectoring nozzle, especially the integration of flight and propulsion system control (IFPSC). So thrust vector modeling is very important and meaningful.
This paper is focused on how to establish mathematical model of vectoring nozzle on the basis of flow field calculation. In order to obtain transient mathematical model as vectoring deflection which is very important in engineering and valuable in theory, three-dimensional and unsteady flow fields must be researched. In our study computational fluid dynamic(CFD) is used to calculate the performance parameters such as the coefficients of mass rate and thrust and efficient deflected angle of the thrust vectoring nozzle. CFD is also used to get the data of performance parameters of the nozzle at different nozzle pressure ratio, different nozzle area ratio and different geometric defected angle. The theory of function approximation is used to establish the transient model of thrust vectoring with the data calculated. The main works and contribution of this paper are as follows:
1.Central type finite volume method proposed by Jameson A. is investigated and the boundary condition of the method is improved. Compared with the testing data it is proved that the program for 3D viscosity steady flow in thrust vectoring nozzle developed is correct and reasonable.
2. More than 200 different condition 3D viscosity steady flow fields in the thrust vectoring nozzle at different nozzle pressure ratio and different nozzle area
ratio and different geometric defected angle is calculated by the program developed. And the related performance parameters are acquired by numerical simulation.
3. The affecting factors of the performance parameters of the thrust vectoring nozzle are investigated. And the affect of nozzle pressure ratio, nozzle area ratio and geometric defected angle on the performance parameters is also investigated.
4. The affect of flow separation on the nozzle is investigated and the macroscopical factor that leads to flow separation is also analyzed.
5. The unsteady flow as thrust vectoring nozzle deflecting dynamically is investigated. The method of calculating the unsteady flow in the nozzle is given and the flow of the nozzle in the maximum power setting and maximum A/B power setting of the engine is calculated.
6. The calculating results of steady flow and unsteady flow in the nozzle are compared. And it proves that both the results of the steady flow and the results of the unsteady .flow are uniform basically. This is very valuable because it is convenient to study the flow in the vectoring nozzle by steady hypothesis or steady test.
7. The upwind finite volume method based on flux vector splitting is investigated, especially the splitting scheme of Steger-Warming, Van Leer, Roe and AUSM+.
8.The method of the parameter fitting based B-spline is investigated. And the method of the parameter fitting which has three free variables is proposed. Based on this method the transient mathematical model of the thrust vectoring nozzle which has three free variables is established.
引文
[1] Benjamin Gal-Or, Western vs Eastern Fighter Technologies Beyond 2000, International Journal of Turbo and Jet Engines, 11,113-118,1994
[2] Benjamin Gal-Or, New Fighter Engines-A Review, Intern.J.Turbo and Jet Engines, 1,183-194,1984
[3] Benjamin Gal-Or, Vectored Propulsion, Super-maneuverability and Robot Aircraft, Book published by Springer Verlag, N,Y., Heidelberg, 1990,1991
[4] Benjamin Gal-Or, Maximizing Post-Stall Thrust-Vectoring Agility and Control Power, AIAA J. Aircraft Vol. 29 No. 4, 647-651, 1992
[5] Benjamin Gal-Or, Thrust Vectoring for Flight Control & Safety: A Review, Intern. J. Turbo and Jet Engines, 11, 1994
[6] 陶增元，李军，程邦勤，飞机推进系统关键技术——推力矢量技术，空军工程大学学报，Vol．1，No．2，Jun．2000
[7] 刘昶，敏捷性、过失速机动、飞机品质和推力矢量控制新进展，南京航空航天大学学报，Vol．30，No．1，Feb．1998
[8] 赵宝凯，推力矢量效益初步研究，飞行力学，Vol．12，No．1，Mar．1994
[9] 申功璋，郝健康，彭可茂，张明廉，综合飞行／推力矢量控制系统设计与仿真，北京航空航天大学学报，Vol．24，No．3，Jun．1998
[10] 刘大响，对加快发展我国航空动力的思考，航空动力学报，Vol．16 No．1，2001年1月
[11] Vivek Sanghi, Engine-Airframe Integration During Conceptual Design for Military Application, Journal of Aircraft,Vol. 35, No. 3, 1998
[12] Shaw P, Haiges K, Skira C, Validation of an integrated flight and propulsion control design for fighter Aircraft, AIAA-87-1928,1987
[13] 卢燕，超音速进气道与矢量喷管数学模型研究，西北工业大学博士学位论文，2002年4月
[14] 马会民，带矢量推力的涡扇发动机实时数学模型及智能控制研究，西北工业大学硕士学位论文，2002年3月
[15] 马会民，樊思齐，涡扇发动机实时数学模型研究，第十届全国航空发动机自动控制会议论文，2000年9月
[16] 樊思齐，马会民，时瑞军，涡扇发动机实时数学模型研究报告，2000年9月
[17] 樊思齐，马会民，卢燕，时瑞军，带推力矢量喷管的涡扇发动机实时数学模型研究报告，2000年9月
[18] 杨小平，孙秀佳，飞机大迎角机动非线性气动力模型的辨识，飞行力学，1998年第一期，1998
[19] 杨新．王小虎，申功璋，文传源，飞机六自由度模型及仿真研究，系统仿真学报，2000年第三期，2000
[20] 史志伟，吴根兴，基于非定常气动力建模的动导数仿真实验，南京航空航天大学学报 1999年05期，1999
[21] George T. Carson, Jr.,and Francis J. Capone, Static Internal performance of Axisymmetric Nozzle With Multiaxis Thrust-Vectoring Capability, NASA TM 4237, 1990
[22] Gal-Or, B. and Sherbaum,V., Thrust Vectoring:Theory, Laboratory and Flight Test-Ⅱ, Israel Aeronautics Conference Proceedings, Feb. 24, 1993, and ASME J. Power, in press. 1993
[23] Gal-Or, B., Novel, Post-Stall, Thrust-Vectored F-15 RPVs: Laboratory, WPAFB. USAF-AFOSR-EOARD, AFOSR 89-0445, April 24, 1990
[24] Gal-Or, B., Tailless Vectored Fighters, Flight Dynamics Directorate, WPAFB, USAF-AFOSR-EOARD, AFOSR 89-0445,July 15,1991
[25] Gal-Or, B., Vectored F-15 and F-22 Flight Dynamics Directorate, WPAFB, USAF-AFOSR-EOARD, F7LEOA-2015S600 & SPC-91-4003,Aug. 31,1992
[26] John S. Orme, etc., Initial Flight Test Evaluation of the F-15 ACTIVE Axisymmetric Vectoring Nozzle Performance, AIAA 98-3871, 1998
[27] Doane, Mark A., Gerard S. Schkolnik, F-15 ACTIVE: A Flexible Propulsion Integration Testbed, AIAA 94-3360, June 1994
[28] Re, R. J. and Leavitt, L. D. Static Internal Performance Including Thrust Vectoring & Reversing of Two-Dimensional Convergent-Divergent Nozzles,NASA TP-2253,1984
[29] John R. Carlson, A Nozzle Internal Performance Prediction Method, NASA Technical Paper 3221,1992
[30] Daniel L. Cler and Mary L. Mason, Ann R. Guthrie. Experimental Investigation of Spherical-convergent-flap Thrust-vectoring Two-dimensional Plug Nozzles. AIAA-93-2431,1993
[31] Swanson, R.C,Navier-Stokes Solutions for Non-axisymmetric Nozzle Flows,AIAA-81-1217
[32] Stevens,H.L. et al. Development of the Multifunction 2-D/C-D Nozzles, AIAA-81-1491,1981
[33] Dusa D.J. et al. Advanced Technology Exhaust Nozzle Development, AIAA-83-1286,1983
[34] Re,R.J.,and Leavitt,L.D. Static Internal Performance Including Thrust Vectoring and Reversing of Two-Dimensional Convergent-Divergent Nozzles,NASA TP-2253,1984
[35] Taylor, J.G., Static Investigation of a Two-Dimensional Convergent-Divergent Exhaust Nozzle with Multiaxis Thrust-Vectoring Capability, NASA TP-2973,1990
[36] Marcarl J.G et al. Performanc Characteristic of a Varible-Area Vane Nozzle for Vectoring an ASTOVL Exhaust Jet Up to 45 Dgrees,AIAA 93-2437,1993
[37] Cler, D.L. et al. Scale Model Test Results for Several Spherical Two-Dimensional Nozzle Concepts, AIAA 93-2430,1993
[38] Milton Lamb. Internal performance characteristics of vectored axisymmetric ejector nozzles. AIAA-93-2432
[39] A. Matesanz, A. Velazquez, M. Rodriguez, Performance Analysis of an Axisymmetric Thrust-Vectoring Nozzle by Using The FUNSIF3D Code, AIAA-95-2743, 1995
[40] A. Matesanz, A. Velázquez and M. Rodriguez. Mach disk simulation in jets from convergent-divergent axisymmetric and thrust vectoring nozzles A. Matesanz, A. Velázquez and M. Rodriguez. AIAA-94-2328,1994
[41] A. Matesanz, A. Velázquez and M. Rodriguez. Numerical study on some fluid dynamics aspects of axisymmetric thrust vectoring nozzles. AIAA-94-3365, 1994
[42] A. Matesanz, A. Velázquez, M. Rodriguez. Performance analysis of an axisymmetric thrust-vectoring nozzle by using the FUNSIF3D code. AIAA-95-2743
[43] Rout.R.H. et al. Three Dimensional Transonic and Supersonic Flow Prediction in Axivectored Nozzles Using a Finite Volume Method,AIAA 90-3367,1990
[44] Capone.F. et al. Comparative Investigation of Multi-pune Thrust Vectoring Nozzles,AIAA 92-3263,1992
[45] 赵桂萍，二元喷管流常三维N—S方程数值计算，西北工业大学硕士学化论文，1993年3月
[44] 扬弘炜等，不同矢量偏角下二元内流特性的数值研究，航空动力学报，Vol．10，No．3，1995
[46] 尤迎玖，进气道三位内流场数值模拟及研究，西北工业大学博士学位论文，1997年6月
[47] 刘小勇，矢量喷管数学模型研究，西北工业大学博士学位论文．1997．6
[48] Yee, H.C, et al, Implicit Total Variation Diminishing(TVD) Schemes for Steady-State Calculations, AIAA 83-1902,1983
[49] Osher, S. et al, Very High Order Accurate TVD Schemes,UCLA Mach. Rept. 1984
[50] Yang, J.Y. Third-Order Nonoscillatory Schemes for Euler Equations,AIAA.J.
Vol.29,No. 10,1991,pp. 1611-1618
[51] 张涵信，无波动、无自由参数、耗散的差分格式，空气动力学学报，Vol．6，No 2，1989
[52] Jameson, A. et al, Numerical Simulation of Euler Equations by Finite Volume Finite Volume Methods Using Runge-Kutta Time-Marching Schemes, AIAA 81-1259,1981
[53] Moitra,A.,Numerical Solution of the Euler Equations for High-Speed Bleeded Wing-Body Configurations, AIAA 85-0123, 1985
[54] Agarwal, R.K., Deese. J. E., Transonic Wing-Body Calculations Using Euler Equations, AIAA 83-0501, 1983
[55] Jameson, A.,Solution of the Euler Equations for Two-Dimensional Transonic Flow by a Multigrid Method, the International Conference in Multigrid, Jun, 1983
[56] Jameson, A. and Bake,T.J. Solution of the Euler Equations for Complex Configurations,AIAA 84-0093,1984
[57] Jameson,A. and Bake,T.J. Multigrid Solution of the Euler Equations for Complex Configrations,AIAA,84-0093,1984
[58] L.He,Three-Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades, Journal of Turbomachinary, Vol-1. 116,P 469,July, 1994
[59] L.He, An Euler Solution for Unsteady Flows Around Oscillating Blades, Transactions of the ASME, Vol. 112,P714,1990
[60] Chi, R. M. An Unsteady Lifting Surface Theory for Ducted fan Blades, ASME Journal of Turbomachines, Vol, 114,pp. 18-26,1990
[61] Avril K.Slone, Dynamic Fluid-structure interactions Using Finite Volume Unstruncted Mesh Procedures, AIAA 2000-4783,2000
[62] Jorgenson P C E, Chima R V. An Unconditionally Stable Runge-Kutta Method for Unsteady Flows,AIAA-89-0205,1989
[63] 白俊强，刘千刚，高正红，绕任意刚性机翼、机翼非定常流动的跨声速欧拉方程解，空气动力学学报，Vol．16，No，2,Jun．1998
[64] Jameson A., Time depended Calculations using Multigrid with Applications to Unsteady Flows past Airfoils and Wings, AIAA 91-1595,1991
[65] 邹正平，徐力平，双重时间步方法在非定常流常模拟中的应用，航空学报，Vol．21,No 4，2000
[66] Martinell,L. Jameson,A. and Grasso,F., A Multigrid Method for the Navier-Stokes Equations,AIAA 86-0208,1986
[67] Johntbatina, Implicit flux Splitting Scheme for Unsteady aerodynamics Analysis Involving Unstruct.ured Dynamic Neshes, N91 10918, 1990
[68] 张智星、孙春在、水谷英二(日)，神经一模糊和软计算，西安交通大学出版社，2000年6月
[70] 徐丽娜，神经网络控制，哈尔滨工业大学出版社，1999年5月
[71] 李士勇，模糊控制 神经控制和智能控制论，哈尔滨工业大学出版社，1998年，9月
[72] 李仁厚，智能控制理论与方法，西安电子科技大学出版社，1999，10
[73] 易继昌等，智能控制技术，北京工业大学出版社，1999年9月
[74] 孙增圻等，智能控制理论与技术，清华大学出版社，1997年4月
[75] Narendra K S and Parthasarathy, Identification and Control tier Dynamic Systems Using Neural Networks, IEEE Trans.on NN, 1990, 1
[76] 张三国，陈希孺，EV多项式模型的估计，中国科学A辑，2001年10期，2001
[77] 徐金光，张懋森，一个新的多项式模型及其在化学中的应用，化学研究与应用，1997年06期，1997
[78] 安振昌，谭东海，东亚地磁场的Taylor多项式模型，地震地磁观测与研究，1994年06期，1994
[79] 黄爱苹，胡荣，基于导频和多项式模型的信道估计，电子学报，2002年04期，2002
[80] 韩大伟，关颖男，赵洪雅，样条函数模型及其A-最优设计，东北大学学报(自然科学版)2001年01期，2001
[81] 郝继升，孙美全，刘彦保，B样条函数网络应用于曲线拟合，延安大学学报(自然科学版)，2000年01期，2000
[82] 陈小平，于盛林，刘文波，基于遗传算法的三次样条函数拟合，数据采集与处理，2000年02期，2000
[83] 李乃宏，吴瑶华，多重共线性诊断及其在飞行器非线性气动模型结构确定和参数估计中的应用，宇航学报，2000年03期，2000
[84] 史忠科，模型在线辨识方法及其应用，控制理论与应用，1995年06期，1995
[85] 汪清，蔡金狮，飞机大攻角气动力建模研究进展，流体力学实验与测量，1994年03期，1994
[86] 王省富，样条函数及其应用，西北工业大学出版社，1989年3月
[87] 蒋大为等，B样条的最小二乘保型光顺逼近，工程数学学报，VOL．17，NO．17,2002
[88] 马铁犹，计算流体力学，北京航空学院出版社，1986年6月
[89] 傅德熏，流体力学数值模拟，国防工业出版社，1994年10月
[90] 朱自强，应用计算流体力学，北京航空航天大学出版社，1998年8月
[91] Thompson J.F., Thomas F.E.,Mastin C.N.,Automatic Numerical Generator of Body-Fitted Curvilinear Coordinate System for Field Containing any Number of Arbitrary Two Dimensional Bodies,Journal of Computional Physics,Vol. 14,1975
[92] 陶文铨，数值传热学，西安交通大学出版社，1995
[93] 封建湖，三维进气道系统流场的数值模拟研究，西北工业大学博士学位论文，1995年3月
[94] A.Jamson, W. Schmidt and E. Turkel. Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes. AIAA—1259, 1981
[95] Jamson A. et al. Solution of the Euler Equations for Complex
Configurations,AIAA 83-1929,1983
[96] Baldwin B S, Lomax H., Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows. AIAA-78-0257
[97] 郑小清，进气道内外流场的计算分析，西北工业大学博士学位论文，1990
[98] 纪永春，喷管内外跨超升速粘性流动的数值研究，北京航空航天大学博士学位论文，1990
[99] Moita,A. Numerical Solution of the Euler Equations for High-Speed BlendedWing-Body Configurations,AIAA 85-0123,1985
[100] Swanson, R.C. Artificial Dissipation and Central Difference Schemes for the Euler Equations, A1AA 87-1107,1986
[101] Moita,A.et al. Application for a Runge-Kutta Scheme for High-Speed Inviscid Internal Flows,AIAA 86-0104,1986
[102] Turkel,E. Acceleration to a Steady for the Euler Equations, NASA CR-172398 1984
[103] Jorgenson P C E, et al. An Unconditionally Stable Runge-Kutta Method for Unsteady Flows,AIAA 89-0205,1989
[104] John R. Carlson, High Reynolds Number Analysis of an Axisymmetric AfterBody with Flow Separation,AIAA 96-2274
[105] Computation of a Shock Wave Boundary Layer interaction in a Nozzle with Different Algorithms and Turbulence Models, AIAA 91-1757
[106] Pauley L.L., A Numerical Investigation of Supersonic Nozzle Boundary Layer Transition, AIAA 91-3559,1991
[107] 刘仪，刘斌，向一敏，扩压器进气道内流及激波／边界层干扰的数值研究，空气动力学学报，Vol．15，No．2，1997．6
[108] F．K．利特尔(美)，内流空气动力学手册(2)，国防工业出版社，1982
[109] G．C．Oates(美)，飞机推进系统技术与设计，航空工业出版社，1992
[110] 高正红，跨音速定常非定常流动的Euler方程解，西北工业博士学位论文，1989
[111] 黄秀全，振动叶栅全三维非定常流动计算，西北工业大学博士学位论文，
2001年5月
[112] 李凤蔚，振动翼型跨音速非定常Euler方程数值解方法，航空学报，Vol．10，No．5，1989
[113] 鄂秦，李凤蔚，复合振动翼型跨音速非定常流计算，空气动力学学报，Vol．8，No．4,1990
[114] 李海东，三维机翼亚音速非定常谐振计算，空气动力学学报，Vol．13，No．2,1995
[115] 董素艳等，多通道涡轮级的流场温度场非定常数值模拟，航空动力学报，2002年第1期
[116] 刘前智等，轴流涡轮机三维粘性非定常流场的双时间法，工程热物理学报，2001年第1期
[117] 刘伟等，非定常超音速流动数值计算方法比较，国防科技大学学报，2001年第1期
[118] 曹从咏等，矢通量分裂隐式三维NND有限体积方法及应用，弹道学报，Vol．12 No．3,2000
[119] 章伯其，Van leer矢通量分裂法求解N—S方程，弹道学报，Vol．7，No．2,1995
[120] Grossman et al., An Analysis of Flux-Split Algorithms for Euler's Equations With Real Gases, AIAA 87-1117,1987
[121] Morrison,J.,Flux Difference Split Scheme for Turbulent Transport Equations, AIAA 90-5251,1990
[122] 谢中强，粘性流场三维NS方程有限体积法数值解，空气动力学学报，Vol．14，No．4，1998
[123] 王正华，矢通量分裂隐式有限体积法解超音速喷流干扰流场，航空学报，Vol．17，No．1．1996
[124] Jon S. Mounts, A Comparison of Explicit and Implicit Three-Dimensional Split Flux Euler Algorithms, AIAA 87-2413,1987
[125] Taylor A.C., An Improved Upwind Finite Volume Relaxation Method for High Speed Viscous Flows, AIAA 89-0549,1989
[126] Stevens R. Allmaras, A Second Order Flux Split Scheme for the Unsteady 2-D
Euler Equations on Arbitrary Meshes, AIAA 87-1119,1987
[127] Casalini, F., A Finite Volume Lambda Formulation,AIAA 91-2258,1991
[128] 邓小刚，NND格式的推广及在粘流计算中的应用，空气动力学学报，Vol．12．No．2 1994
[129] J.C. Wang, A Three-Dimensional, Finite Volume TVD Scheme tbr Geometrically Complex Steady and Transient Flows,AIAA 88-0228,1988
[130] S.T. Chiang, Comparison of Flux-vector Splitting Schemes for Finite Diferencc and Finite Volume Techniques, AIAA 91-0170,1991
[131] Rossow, C.-C., A Flux Splitting Scheme Compressible and Incompressible Flows, AIAA 99-3346,1999
[132] Steger, J.L.,Warming,R.F.,Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite Difference Methods, Journal ot Computational Physics, Vol.40, No.2, pp. 263-293, 1981
[133] Steger, J.L. Preliminary Study of Relaxation Methods for the Inviscid Conservative Gas dynamics Equations Using Flux Splitting, NASA CR-3415,1981
[134] Datta Gaitonde, A Numerical Study of Viscous Shock-on-Shock Hypersonic Flows with a Modified Steger-Warming Flux Split Schemes, AIAA 90-1491,1991
[135] Van Leer, B.,Flux-Vector Splitting for the Euler Equations, Lectures Notes in Physics, Vol.170, pp. 507-512,1982
[136] Van Leer, B., Towards the Ultimate Conservative Difference Scheme V a Second Order Sequal to Gudonov's Method, Journal of Computational Physics, Vol.32, pp. 101-136, 1979
[137] Van Leer, B. A Comparison of Numerical Flux Formulas for the Euler and N avier-Stokes Eq uations,AIAA 87-1104,1987
[138] Anderson,W.K., A Comparison of Finite Volume Flux Vector Splitting for the Euler Equations, AIAA 85-0122,1985
[139] Ge-Cheng Zha, Comparative Study of Upwind Scheme Performance for Entropy Condition and Discontinuities,AIAA 99-3348,1999
[140] Roe,P.L., Approximate Riemann Solvers, Parameter Vectors and Difference Scheme, Journal of Computational Physics, Vol.43, pp.357, 1981
[141] Roe,P.L., et al., Efficient Construction and Utilization of Approximate Riemann Solutions, Computing Methods in Applied Science and Engineering, 1984
[142] Roe,P.L., Characteristic-based Schemes for the Euler Equations,Fluid Mechnic, 1986-18, pp 337-365
[143] R.Radespiel, Accurate Flux Vector Splitting for Shocks and Shear layers, Journal of Computational Physics, Vol. 121, 66-78,, 1995
[144] Meng-Sing Liou, A Sequel to AUSM: AUSM+, Journal of Computational Physics, Vol. 129, pp.364-382,, 1996
[145] Meng-Sing Liou, Progress Towards an Improved CFD Methods: AUSM~+,AIAA 95-1701-CP,1995
[146] Meng-Sing Liou, et al. A New Flux Splitting Scheme, Journal of Computational Physics, Vol. 107,pp. 1-23,, 1993
[147] Muler W.A., Van Leer B., Implicit Upwind methods for the Euler equations, AIAA 83-1930-1983
[148] Koren B., Upwind Schemes Multigrid and Defect Correction for Steady Navier-Stokes equations, AIAA 83-1930,1983
[150] 沈燮昌，多项式最佳逼近的实现，上海科学技术出版社，1981年10月
[151] 赵元民，函数逼近方法，科学出版社，1981年10月
[152] 李岳生，齐东旭，样条函数方法，科学出版社，1979
[153] 黄友谦，曲线曲面的数值表示和逼近，上海科学技术出版社，1984年9月
[2] Benjamin Gal-Or, New Fighter Engines-A Review, Intern.J.Turbo and Jet Engines, 1,183-194,1984
[3] Benjamin Gal-Or, Vectored Propulsion, Super-maneuverability and Robot Aircraft, Book published by Springer Verlag, N,Y., Heidelberg, 1990,1991
[4] Benjamin Gal-Or, Maximizing Post-Stall Thrust-Vectoring Agility and Control Power, AIAA J. Aircraft Vol. 29 No. 4, 647-651, 1992
[5] Benjamin Gal-Or, Thrust Vectoring for Flight Control & Safety: A Review, Intern. J. Turbo and Jet Engines, 11, 1994
[6] 陶增元，李军，程邦勤，飞机推进系统关键技术——推力矢量技术，空军工程大学学报，Vol．1，No．2，Jun．2000
[7] 刘昶，敏捷性、过失速机动、飞机品质和推力矢量控制新进展，南京航空航天大学学报，Vol．30，No．1，Feb．1998
[8] 赵宝凯，推力矢量效益初步研究，飞行力学，Vol．12，No．1，Mar．1994
[9] 申功璋，郝健康，彭可茂，张明廉，综合飞行／推力矢量控制系统设计与仿真，北京航空航天大学学报，Vol．24，No．3，Jun．1998
[10] 刘大响，对加快发展我国航空动力的思考，航空动力学报，Vol．16 No．1，2001年1月
[11] Vivek Sanghi, Engine-Airframe Integration During Conceptual Design for Military Application, Journal of Aircraft,Vol. 35, No. 3, 1998
[12] Shaw P, Haiges K, Skira C, Validation of an integrated flight and propulsion control design for fighter Aircraft, AIAA-87-1928,1987
[13] 卢燕，超音速进气道与矢量喷管数学模型研究，西北工业大学博士学位论文，2002年4月
[14] 马会民，带矢量推力的涡扇发动机实时数学模型及智能控制研究，西北工业大学硕士学位论文，2002年3月
[15] 马会民，樊思齐，涡扇发动机实时数学模型研究，第十届全国航空发动机自动控制会议论文，2000年9月
[16] 樊思齐，马会民，时瑞军，涡扇发动机实时数学模型研究报告，2000年9月
[17] 樊思齐，马会民，卢燕，时瑞军，带推力矢量喷管的涡扇发动机实时数学模型研究报告，2000年9月
[18] 杨小平，孙秀佳，飞机大迎角机动非线性气动力模型的辨识，飞行力学，1998年第一期，1998
[19] 杨新．王小虎，申功璋，文传源，飞机六自由度模型及仿真研究，系统仿真学报，2000年第三期，2000
[20] 史志伟，吴根兴，基于非定常气动力建模的动导数仿真实验，南京航空航天大学学报 1999年05期，1999
[21] George T. Carson, Jr.,and Francis J. Capone, Static Internal performance of Axisymmetric Nozzle With Multiaxis Thrust-Vectoring Capability, NASA TM 4237, 1990
[22] Gal-Or, B. and Sherbaum,V., Thrust Vectoring:Theory, Laboratory and Flight Test-Ⅱ, Israel Aeronautics Conference Proceedings, Feb. 24, 1993, and ASME J. Power, in press. 1993
[23] Gal-Or, B., Novel, Post-Stall, Thrust-Vectored F-15 RPVs: Laboratory, WPAFB. USAF-AFOSR-EOARD, AFOSR 89-0445, April 24, 1990
[24] Gal-Or, B., Tailless Vectored Fighters, Flight Dynamics Directorate, WPAFB, USAF-AFOSR-EOARD, AFOSR 89-0445,July 15,1991
[25] Gal-Or, B., Vectored F-15 and F-22 Flight Dynamics Directorate, WPAFB, USAF-AFOSR-EOARD, F7LEOA-2015S600 & SPC-91-4003,Aug. 31,1992
[26] John S. Orme, etc., Initial Flight Test Evaluation of the F-15 ACTIVE Axisymmetric Vectoring Nozzle Performance, AIAA 98-3871, 1998
[27] Doane, Mark A., Gerard S. Schkolnik, F-15 ACTIVE: A Flexible Propulsion Integration Testbed, AIAA 94-3360, June 1994
[28] Re, R. J. and Leavitt, L. D. Static Internal Performance Including Thrust Vectoring & Reversing of Two-Dimensional Convergent-Divergent Nozzles,NASA TP-2253,1984
[29] John R. Carlson, A Nozzle Internal Performance Prediction Method, NASA Technical Paper 3221,1992
[30] Daniel L. Cler and Mary L. Mason, Ann R. Guthrie. Experimental Investigation of Spherical-convergent-flap Thrust-vectoring Two-dimensional Plug Nozzles. AIAA-93-2431,1993
[31] Swanson, R.C,Navier-Stokes Solutions for Non-axisymmetric Nozzle Flows,AIAA-81-1217
[32] Stevens,H.L. et al. Development of the Multifunction 2-D/C-D Nozzles, AIAA-81-1491,1981
[33] Dusa D.J. et al. Advanced Technology Exhaust Nozzle Development, AIAA-83-1286,1983
[34] Re,R.J.,and Leavitt,L.D. Static Internal Performance Including Thrust Vectoring and Reversing of Two-Dimensional Convergent-Divergent Nozzles,NASA TP-2253,1984
[35] Taylor, J.G., Static Investigation of a Two-Dimensional Convergent-Divergent Exhaust Nozzle with Multiaxis Thrust-Vectoring Capability, NASA TP-2973,1990
[36] Marcarl J.G et al. Performanc Characteristic of a Varible-Area Vane Nozzle for Vectoring an ASTOVL Exhaust Jet Up to 45 Dgrees,AIAA 93-2437,1993
[37] Cler, D.L. et al. Scale Model Test Results for Several Spherical Two-Dimensional Nozzle Concepts, AIAA 93-2430,1993
[38] Milton Lamb. Internal performance characteristics of vectored axisymmetric ejector nozzles. AIAA-93-2432
[39] A. Matesanz, A. Velazquez, M. Rodriguez, Performance Analysis of an Axisymmetric Thrust-Vectoring Nozzle by Using The FUNSIF3D Code, AIAA-95-2743, 1995
[40] A. Matesanz, A. Velázquez and M. Rodriguez. Mach disk simulation in jets from convergent-divergent axisymmetric and thrust vectoring nozzles A. Matesanz, A. Velázquez and M. Rodriguez. AIAA-94-2328,1994
[41] A. Matesanz, A. Velázquez and M. Rodriguez. Numerical study on some fluid dynamics aspects of axisymmetric thrust vectoring nozzles. AIAA-94-3365, 1994
[42] A. Matesanz, A. Velázquez, M. Rodriguez. Performance analysis of an axisymmetric thrust-vectoring nozzle by using the FUNSIF3D code. AIAA-95-2743
[43] Rout.R.H. et al. Three Dimensional Transonic and Supersonic Flow Prediction in Axivectored Nozzles Using a Finite Volume Method,AIAA 90-3367,1990
[44] Capone.F. et al. Comparative Investigation of Multi-pune Thrust Vectoring Nozzles,AIAA 92-3263,1992
[45] 赵桂萍，二元喷管流常三维N—S方程数值计算，西北工业大学硕士学化论文，1993年3月
[44] 扬弘炜等，不同矢量偏角下二元内流特性的数值研究，航空动力学报，Vol．10，No．3，1995
[46] 尤迎玖，进气道三位内流场数值模拟及研究，西北工业大学博士学位论文，1997年6月
[47] 刘小勇，矢量喷管数学模型研究，西北工业大学博士学位论文．1997．6
[48] Yee, H.C, et al, Implicit Total Variation Diminishing(TVD) Schemes for Steady-State Calculations, AIAA 83-1902,1983
[49] Osher, S. et al, Very High Order Accurate TVD Schemes,UCLA Mach. Rept. 1984
[50] Yang, J.Y. Third-Order Nonoscillatory Schemes for Euler Equations,AIAA.J.
Vol.29,No. 10,1991,pp. 1611-1618
[51] 张涵信，无波动、无自由参数、耗散的差分格式，空气动力学学报，Vol．6，No 2，1989
[52] Jameson, A. et al, Numerical Simulation of Euler Equations by Finite Volume Finite Volume Methods Using Runge-Kutta Time-Marching Schemes, AIAA 81-1259,1981
[53] Moitra,A.,Numerical Solution of the Euler Equations for High-Speed Bleeded Wing-Body Configurations, AIAA 85-0123, 1985
[54] Agarwal, R.K., Deese. J. E., Transonic Wing-Body Calculations Using Euler Equations, AIAA 83-0501, 1983
[55] Jameson, A.,Solution of the Euler Equations for Two-Dimensional Transonic Flow by a Multigrid Method, the International Conference in Multigrid, Jun, 1983
[56] Jameson, A. and Bake,T.J. Solution of the Euler Equations for Complex Configurations,AIAA 84-0093,1984
[57] Jameson,A. and Bake,T.J. Multigrid Solution of the Euler Equations for Complex Configrations,AIAA,84-0093,1984
[58] L.He,Three-Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades, Journal of Turbomachinary, Vol-1. 116,P 469,July, 1994
[59] L.He, An Euler Solution for Unsteady Flows Around Oscillating Blades, Transactions of the ASME, Vol. 112,P714,1990
[60] Chi, R. M. An Unsteady Lifting Surface Theory for Ducted fan Blades, ASME Journal of Turbomachines, Vol, 114,pp. 18-26,1990
[61] Avril K.Slone, Dynamic Fluid-structure interactions Using Finite Volume Unstruncted Mesh Procedures, AIAA 2000-4783,2000
[62] Jorgenson P C E, Chima R V. An Unconditionally Stable Runge-Kutta Method for Unsteady Flows,AIAA-89-0205,1989
[63] 白俊强，刘千刚，高正红，绕任意刚性机翼、机翼非定常流动的跨声速欧拉方程解，空气动力学学报，Vol．16，No，2,Jun．1998
[64] Jameson A., Time depended Calculations using Multigrid with Applications to Unsteady Flows past Airfoils and Wings, AIAA 91-1595,1991
[65] 邹正平，徐力平，双重时间步方法在非定常流常模拟中的应用，航空学报，Vol．21,No 4，2000
[66] Martinell,L. Jameson,A. and Grasso,F., A Multigrid Method for the Navier-Stokes Equations,AIAA 86-0208,1986
[67] Johntbatina, Implicit flux Splitting Scheme for Unsteady aerodynamics Analysis Involving Unstruct.ured Dynamic Neshes, N91 10918, 1990
[68] 张智星、孙春在、水谷英二(日)，神经一模糊和软计算，西安交通大学出版社，2000年6月
[70] 徐丽娜，神经网络控制，哈尔滨工业大学出版社，1999年5月
[71] 李士勇，模糊控制 神经控制和智能控制论，哈尔滨工业大学出版社，1998年，9月
[72] 李仁厚，智能控制理论与方法，西安电子科技大学出版社，1999，10
[73] 易继昌等，智能控制技术，北京工业大学出版社，1999年9月
[74] 孙增圻等，智能控制理论与技术，清华大学出版社，1997年4月
[75] Narendra K S and Parthasarathy, Identification and Control tier Dynamic Systems Using Neural Networks, IEEE Trans.on NN, 1990, 1
[76] 张三国，陈希孺，EV多项式模型的估计，中国科学A辑，2001年10期，2001
[77] 徐金光，张懋森，一个新的多项式模型及其在化学中的应用，化学研究与应用，1997年06期，1997
[78] 安振昌，谭东海，东亚地磁场的Taylor多项式模型，地震地磁观测与研究，1994年06期，1994
[79] 黄爱苹，胡荣，基于导频和多项式模型的信道估计，电子学报，2002年04期，2002
[80] 韩大伟，关颖男，赵洪雅，样条函数模型及其A-最优设计，东北大学学报(自然科学版)2001年01期，2001
[81] 郝继升，孙美全，刘彦保，B样条函数网络应用于曲线拟合，延安大学学报(自然科学版)，2000年01期，2000
[82] 陈小平，于盛林，刘文波，基于遗传算法的三次样条函数拟合，数据采集与处理，2000年02期，2000
[83] 李乃宏，吴瑶华，多重共线性诊断及其在飞行器非线性气动模型结构确定和参数估计中的应用，宇航学报，2000年03期，2000
[84] 史忠科，模型在线辨识方法及其应用，控制理论与应用，1995年06期，1995
[85] 汪清，蔡金狮，飞机大攻角气动力建模研究进展，流体力学实验与测量，1994年03期，1994
[86] 王省富，样条函数及其应用，西北工业大学出版社，1989年3月
[87] 蒋大为等，B样条的最小二乘保型光顺逼近，工程数学学报，VOL．17，NO．17,2002
[88] 马铁犹，计算流体力学，北京航空学院出版社，1986年6月
[89] 傅德熏，流体力学数值模拟，国防工业出版社，1994年10月
[90] 朱自强，应用计算流体力学，北京航空航天大学出版社，1998年8月
[91] Thompson J.F., Thomas F.E.,Mastin C.N.,Automatic Numerical Generator of Body-Fitted Curvilinear Coordinate System for Field Containing any Number of Arbitrary Two Dimensional Bodies,Journal of Computional Physics,Vol. 14,1975
[92] 陶文铨，数值传热学，西安交通大学出版社，1995
[93] 封建湖，三维进气道系统流场的数值模拟研究，西北工业大学博士学位论文，1995年3月
[94] A.Jamson, W. Schmidt and E. Turkel. Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes. AIAA—1259, 1981
[95] Jamson A. et al. Solution of the Euler Equations for Complex
Configurations,AIAA 83-1929,1983
[96] Baldwin B S, Lomax H., Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows. AIAA-78-0257
[97] 郑小清，进气道内外流场的计算分析，西北工业大学博士学位论文，1990
[98] 纪永春，喷管内外跨超升速粘性流动的数值研究，北京航空航天大学博士学位论文，1990
[99] Moita,A. Numerical Solution of the Euler Equations for High-Speed BlendedWing-Body Configurations,AIAA 85-0123,1985
[100] Swanson, R.C. Artificial Dissipation and Central Difference Schemes for the Euler Equations, A1AA 87-1107,1986
[101] Moita,A.et al. Application for a Runge-Kutta Scheme for High-Speed Inviscid Internal Flows,AIAA 86-0104,1986
[102] Turkel,E. Acceleration to a Steady for the Euler Equations, NASA CR-172398 1984
[103] Jorgenson P C E, et al. An Unconditionally Stable Runge-Kutta Method for Unsteady Flows,AIAA 89-0205,1989
[104] John R. Carlson, High Reynolds Number Analysis of an Axisymmetric AfterBody with Flow Separation,AIAA 96-2274
[105] Computation of a Shock Wave Boundary Layer interaction in a Nozzle with Different Algorithms and Turbulence Models, AIAA 91-1757
[106] Pauley L.L., A Numerical Investigation of Supersonic Nozzle Boundary Layer Transition, AIAA 91-3559,1991
[107] 刘仪，刘斌，向一敏，扩压器进气道内流及激波／边界层干扰的数值研究，空气动力学学报，Vol．15，No．2，1997．6
[108] F．K．利特尔(美)，内流空气动力学手册(2)，国防工业出版社，1982
[109] G．C．Oates(美)，飞机推进系统技术与设计，航空工业出版社，1992
[110] 高正红，跨音速定常非定常流动的Euler方程解，西北工业博士学位论文，1989
[111] 黄秀全，振动叶栅全三维非定常流动计算，西北工业大学博士学位论文，
2001年5月
[112] 李凤蔚，振动翼型跨音速非定常Euler方程数值解方法，航空学报，Vol．10，No．5，1989
[113] 鄂秦，李凤蔚，复合振动翼型跨音速非定常流计算，空气动力学学报，Vol．8，No．4,1990
[114] 李海东，三维机翼亚音速非定常谐振计算，空气动力学学报，Vol．13，No．2,1995
[115] 董素艳等，多通道涡轮级的流场温度场非定常数值模拟，航空动力学报，2002年第1期
[116] 刘前智等，轴流涡轮机三维粘性非定常流场的双时间法，工程热物理学报，2001年第1期
[117] 刘伟等，非定常超音速流动数值计算方法比较，国防科技大学学报，2001年第1期
[118] 曹从咏等，矢通量分裂隐式三维NND有限体积方法及应用，弹道学报，Vol．12 No．3,2000
[119] 章伯其，Van leer矢通量分裂法求解N—S方程，弹道学报，Vol．7，No．2,1995
[120] Grossman et al., An Analysis of Flux-Split Algorithms for Euler's Equations With Real Gases, AIAA 87-1117,1987
[121] Morrison,J.,Flux Difference Split Scheme for Turbulent Transport Equations, AIAA 90-5251,1990
[122] 谢中强，粘性流场三维NS方程有限体积法数值解，空气动力学学报，Vol．14，No．4，1998
[123] 王正华，矢通量分裂隐式有限体积法解超音速喷流干扰流场，航空学报，Vol．17，No．1．1996
[124] Jon S. Mounts, A Comparison of Explicit and Implicit Three-Dimensional Split Flux Euler Algorithms, AIAA 87-2413,1987
[125] Taylor A.C., An Improved Upwind Finite Volume Relaxation Method for High Speed Viscous Flows, AIAA 89-0549,1989
[126] Stevens R. Allmaras, A Second Order Flux Split Scheme for the Unsteady 2-D
Euler Equations on Arbitrary Meshes, AIAA 87-1119,1987
[127] Casalini, F., A Finite Volume Lambda Formulation,AIAA 91-2258,1991
[128] 邓小刚，NND格式的推广及在粘流计算中的应用，空气动力学学报，Vol．12．No．2 1994
[129] J.C. Wang, A Three-Dimensional, Finite Volume TVD Scheme tbr Geometrically Complex Steady and Transient Flows,AIAA 88-0228,1988
[130] S.T. Chiang, Comparison of Flux-vector Splitting Schemes for Finite Diferencc and Finite Volume Techniques, AIAA 91-0170,1991
[131] Rossow, C.-C., A Flux Splitting Scheme Compressible and Incompressible Flows, AIAA 99-3346,1999
[132] Steger, J.L.,Warming,R.F.,Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite Difference Methods, Journal ot Computational Physics, Vol.40, No.2, pp. 263-293, 1981
[133] Steger, J.L. Preliminary Study of Relaxation Methods for the Inviscid Conservative Gas dynamics Equations Using Flux Splitting, NASA CR-3415,1981
[134] Datta Gaitonde, A Numerical Study of Viscous Shock-on-Shock Hypersonic Flows with a Modified Steger-Warming Flux Split Schemes, AIAA 90-1491,1991
[135] Van Leer, B.,Flux-Vector Splitting for the Euler Equations, Lectures Notes in Physics, Vol.170, pp. 507-512,1982
[136] Van Leer, B., Towards the Ultimate Conservative Difference Scheme V a Second Order Sequal to Gudonov's Method, Journal of Computational Physics, Vol.32, pp. 101-136, 1979
[137] Van Leer, B. A Comparison of Numerical Flux Formulas for the Euler and N avier-Stokes Eq uations,AIAA 87-1104,1987
[138] Anderson,W.K., A Comparison of Finite Volume Flux Vector Splitting for the Euler Equations, AIAA 85-0122,1985
[139] Ge-Cheng Zha, Comparative Study of Upwind Scheme Performance for Entropy Condition and Discontinuities,AIAA 99-3348,1999
[140] Roe,P.L., Approximate Riemann Solvers, Parameter Vectors and Difference Scheme, Journal of Computational Physics, Vol.43, pp.357, 1981
[141] Roe,P.L., et al., Efficient Construction and Utilization of Approximate Riemann Solutions, Computing Methods in Applied Science and Engineering, 1984
[142] Roe,P.L., Characteristic-based Schemes for the Euler Equations,Fluid Mechnic, 1986-18, pp 337-365
[143] R.Radespiel, Accurate Flux Vector Splitting for Shocks and Shear layers, Journal of Computational Physics, Vol. 121, 66-78,, 1995
[144] Meng-Sing Liou, A Sequel to AUSM: AUSM+, Journal of Computational Physics, Vol. 129, pp.364-382,, 1996
[145] Meng-Sing Liou, Progress Towards an Improved CFD Methods: AUSM~+,AIAA 95-1701-CP,1995
[146] Meng-Sing Liou, et al. A New Flux Splitting Scheme, Journal of Computational Physics, Vol. 107,pp. 1-23,, 1993
[147] Muler W.A., Van Leer B., Implicit Upwind methods for the Euler equations, AIAA 83-1930-1983
[148] Koren B., Upwind Schemes Multigrid and Defect Correction for Steady Navier-Stokes equations, AIAA 83-1930,1983
[150] 沈燮昌，多项式最佳逼近的实现，上海科学技术出版社，1981年10月
[151] 赵元民，函数逼近方法，科学出版社，1981年10月
[152] 李岳生，齐东旭，样条函数方法，科学出版社，1979
[153] 黄友谦，曲线曲面的数值表示和逼近，上海科学技术出版社，1984年9月