超音速边界层稳定性及其高阶激波捕捉格式研究
|
摘要
随着航空航天事业的发展,(高)超音速飞行器越来越多。层流和湍流的差异所导致的气动力、气动热以及气动噪声等的明显不同直接影响着飞行器的性能与安全,而目前对(高)超音速边界层的稳定性以及转捩的了解很少。(高)超音速边界层稳定性研究非常具有挑战意义,因为实验代价高且不易实现,受计算方法和计算机速度和内存的限制,计算也有一定困难,而理论研究在一百多年来还是进展缓慢。超音速与低速最大的不同之一便是激波,比如激波与边界层干扰,甚至在边界层失稳过程中还可能存在小激波,所以要求计算格式既能光滑无振荡地捕捉激波,又必须具有相当高精度以保证能精确描述边界层内不稳定因素的微小变化。本文首先从有限差分格式出发,发展出了基本无振荡的高阶激波捕捉格式,然后,我们采用抛物化稳定性研究方法以及直接数值模拟(DNS)方法等对超音速边界层的稳定性进行了研究。
在计算格式方面:(1)给出了一种TVD格式的判据,TVD格式的构造方法以及相应的TVD限制器。这种方法可以很简单地把不能光滑捕捉激波的线性格式改装成能够基本光滑捕捉的非线性TVD格式。计算表明,这类TVD格式总体上能保证原始线性格式的精度,而且不会影响原格式的尺度分辨率。(2)讨论了线性紧致格式,列出了一阶至八阶线性紧致格式的系数所应该满足的条件,并采用Fourier方法对格式的精度和分辨率进行分析,结果表明紧致格式不仅具有较高精度,还具有优于传统单点显式差分的高分辨率(保频谱性)。(3)把紧致格式改写成重构函数的形式(表达在网格单元中心上),同时给出了一种紧致重构函数的边界处理方法,稳定性分析表明,这些格式是渐进稳定的。(4)发展出了适用于双曲系统的紧致TVD格式以及特征型紧致TVD格式。(5)通过大量算例着重考察了特征型紧致TVD格式的精度,并与文献中的高阶格式进行了一些比较,发现本文格式具有精度高,虚假波动小,对流场细小结构的刻画能力强等优点。
本文还对格式精度、网格和CFD不确定度进行了简单考察。计算表明,若采用二阶格式,压力计算很容易达到两位真值准确,但是,除非网格极密,摩擦阻力很难达到两位真值准确。采用高阶格式可以提高计算结果的置信度,而且压力基本能达到三位真值准确。在摩阻和热流方面,计算达到两位真值准确是相对比较容易实现的,但是要想达到三位真值准确,高阶格式已经很难,低阶格式就更难。
在稳定性研究方面,本文采用抛物化稳定性方程(PSE)研究了二维超音速边界层的线性和非线性稳定性,并对PSE的特征值进行了分析,发现了一些文献中没有发现的现象,比如PSE的主特征值除了一个为v/u外,其余都为零。PSE的次特征与流向波数α有关。若α=0,则次特征为抛物-双曲型。若α的实部不为零,则必然会出现复特征值,即当扰动在流向存在波动性时,必定会在稳定性方程中导致椭圆性。若α的虚部的绝对值超过某个临界值,仍然可能在稳定性方程中导致椭圆性。根据参考文献,目前主要有两种方法可以克服PSE的椭圆性,一种是对压力扰动采取修正,另一种是采用较大的空间推进步长。
本文发展出了PSE的算法,采用PSE对Ma = 4.5的平板边界层的稳定性问题进行了研究,并用DNS验证了本文研究方法的正确性。通过与DNS和LST的比较,发现PSE的计算效率最高,而且计算精度基本与DNS相当。通过采用二维非线性PSE对边界层稳定性的研究,发现随着基本扰动的增大,会出现以下非线性现象:(1)稳定的高阶谐波会变得不稳定;(2)基频扰动幅值越大,失稳的高阶谐波越多,谐波的增长速度越快;(3)高阶谐波失稳的位置随着基频扰动幅值的增大而向上游移动;(4)高阶谐波增长有向饱和状态发展的趋势;(5)从涡量上看,大涡向小涡破碎,在临界层内的小涡更加丰富,大涡和小涡以及小涡和小涡之间相互作用,使得临界层内的涡量增长更快。本文发展出了三维PSE的算法,并采用三维线性PSE进行了稳定性研究,发现: (1)二维波可以自动调制出展向扰动,而且展向扰动的增长速度比其它扰动更快; (2)展向扰动呈现出两个极值点,一个在紧靠壁面的附近,另一个更大的极值点在临界层附近,临界层内的展向扰动等值线向前倾斜分布; (3)当采用数值方法进行稳定性分析时,网格密度应该与波矢方向上的波长相匹配。
本文最后还采用DNS方法研究了(1)激波-边界层相互作用对小扰动传播的影响和(2)法向速度扰动在2度攻角高超音速钝锥中的演化。一个斜激波被入射到Ma=4.5的平板边界层上,与边界层相互作用诱导分离等复杂流动结构,并对小扰动的传播存在非常大的影响。本文发现分离区不仅对扰动波具有抑制作用,同时,还会激发出新的低频扰动;在分离区内扰动呈现出第二模式的特征;激波和边界层加厚会使扰动波的传播速度变慢;激波与分离对扰动波的影响并不局限在激波两侧和分离区内,都存在着相应的影响区域。通过对2度攻角高超音速钝锥的稳定性计算发现,由于攻角的存在,钝锥的稳定性特征与零攻角时有本质的差别,比如背风面的扰动比迎风面增长更快,但扰增长最慢的地方并不是迎风面,而是侧面的某个位置;又比如背风面主要是长波起作用,迎风面和侧面主要是短波起作用;斜模式不稳定在整个钝锥边界层中起最主要的作用。
With the continuous development of aeronautic and astronautic technology, there are more and more supersonic and hypersonic aero/space crafts. The essential difference between laminar flow and turbulent flow causes large changes in aerodynamic force and heat as well as noise, which has vital effect on the performance and safety of the crafts. However, the achievements on supersonic/hypersonic boundary layer instability and laminar to turbulent transition are still limited. The study of the instability of supersonic/hypersonic flows is a tough task because of the following difficulties: it is very difficult to simulate this kind of flight environments in wind tunnels, and the experiment costs are expensive; direct numerical simulations (DNS) are restrained for the limitation of computing speed and RAM capability; theoretical studies about fluid instability were advancing very slowly for more than 100 years. The existence of shock waves in high-speed flows makes things much harder, such as shock-boundary interactions. Furthermore, small-structure shock waves may come into being during the instability process. Numerical algorithms should not only smoothly capture discontinuities, but also preserve favorable high-order accuracy in order to accurate simulating every trivial instability factors. A kind of nonoscillatory high-order shock-capturing finite difference schemes is formulated in this paper. Parabolized stability equations (PSE) and DNS are employed to study the instability of supersonic/hypersonic boundary layers.
The following works about high-order schemes have been done: (1) Works about TVD schemes including a new TVD criterion, TVD limiters, and a new method transforming linear schemes into TVD ones. Numerical tests show that this kind of TVD schemes can generally hold the high-order accuracy of their original linear schemes, and the limiters have no effect on resolution properties. (2) Linear compact schemes are reviewed. A class of compact schemes from 1st order to 7th order is given. The accuracy and resolution power of some high-order schemes are studied by Fourier analysis method. The results show that compact schemes possess the advantage of high-order accuracy and high resolution compared with the traditional schemes. (3) Compact schemes are converted into reconstruction forms (at cell center). Boundary closure is given for compact reconstruction functions. Stability analysis shows that the schemes are linearly stable. (4) Compact-TVD schemes and characteristic-based compact-TVD schemes are devised for hyperbolic systems. (5) The properties of the characteristic-based compact-TVD schemes are checked on some benchmark problems in one, two and three space dimensions. Our results are compared with those of other high-order schemes, and the results show that our schemes are high-order accurate with high resolution and less oscillatory.
The relations among CFD uncertainty, grid and numerical discrete accuracy are discussed. Our results indicate that pressure will easily reach two-digital virtual value accuracy even by lower order numerical schemes (2nd order). However, if the scheme is a 2nd order one, friction can hardly reach two-digital virtual value accuracy except that the grid is enough refined. High-order schemes (at less 3rd order) show advantages in improving the probability of accurate computing. If higher order schemes are used, pressure can even reach three-digital virtual value accuracy. Generally speaking, present numerical means can relatively easily reach two-digital virtual value accuracy, while three-digital virtual value accuracy is a tough goal for high-order schemes, and a much harder task for lower order schemes.
Linear and nonlinear stability of 2D supersonic boundary layers is studied using PSE. Characteristics analysis shows some special aspects which are ignored in literatures in the references. The main characteristics of PSE are zero except v/u. The second characteristics of PSE are related to the complex wave numberα. Ifαis zero, the PSE with their second characteristics are parabolic-hyperbolic. If the real part ofαis nonzero, two or more complex characteristics must appear. If the ABS of the image part ofαis greater than a critical number, a pair of conjugate complex number would appear in the second characteristics. There are mainly two ways to suppress the ellipticity of PSE: by modifying the pressure-gradient term of the pressure disturbance or by employing large marching steps.
The discretization formulas are given for PSE. PSE are employed to study the stability of a Ma = 4.5 planar plate boundary layer, and its correctness is confirmed by DNS. Compared with LST and DNS, linear and nonlinear PSE calculations yield results that are in good agreement with that of DNS, while the computational cost of PSE is the lowest among the three. The nonlinear PSE calculations show that the following nonlinear phenomena will emerge with every enhanced initial disturbance: (1) The stable harmonic waves will become unstable; (2) The larger the basic disturbance is, the more unstable harmonic waves there will be, and the faster the increasing speed of the unstable harmonic waves will become; (3) The critical positions where the harmonic waves become unstable are moving upwind with the increasing amplitude of the basic disturbance; (4) Harmonic waves are likely to reach a saturation state; (5) Large scale vortices will break down into small scale vortices, which makes the critical layer filled with abundant small scale vortices, and the mutually interaction of vortices results in that the vortices increase their amplitude more fast.
The algorithms for solving 3D PSE are developed. 3D linear PSE is applied to study the stability performance of a boundary layer. The results show that: (1) 2D waves will self-modulate a transverse disturbance, and the transverse disturbance increases faster than the 2D waves; (2) Two extreme points are found on the transverse disturbance, the smaller one is closer to the wall, while the larger one is in the critical layer; (3) When numerical methods are applied to study fluids instabilities, the grid size shall be allocated in according to the wavewise wavelength instead of the streamwise wavelength.
The stabilities of shock-boundary interaction and a hypersonic blunt cone at 2 degree angle of attack (AOA) are studied by DNS. An oblique shock wave is imposed on a two dimensional laminar Ma = 4.5 flow. A separation bubble forms between the shock wave and the solid plane, and the bubble causes compressing waves, expansion waves and a vortex. These complex flow structures have great influence on the stability. We find that the separation bubble can not only make the disturbance stable, but also modulate lower frequency waves. Second mode instability is found in the separation bubble. The travel speed of the disturbance is slowed down by the conjoint influence of the shock and the thickened boundary layer. The influence regions of the shock and the separation bubble are far more than the shock and the bubble themselves. Another DNS study is the evolutions of a vertical velocity disturbance in the boundary layer of the hypersonic cone at 2 degree AOA. The results show that the stability characters are quite different from cases without AOA. The leeward boundary is more unstable than the windward boundary. The most stable position is not in the windward, but in the sideward. The unstable waves in the leeward are mainly long waves, while the unstable waves in the windward and sideward are shorter ones. The main instability mechanism is an oblique model.
在计算格式方面:(1)给出了一种TVD格式的判据,TVD格式的构造方法以及相应的TVD限制器。这种方法可以很简单地把不能光滑捕捉激波的线性格式改装成能够基本光滑捕捉的非线性TVD格式。计算表明,这类TVD格式总体上能保证原始线性格式的精度,而且不会影响原格式的尺度分辨率。(2)讨论了线性紧致格式,列出了一阶至八阶线性紧致格式的系数所应该满足的条件,并采用Fourier方法对格式的精度和分辨率进行分析,结果表明紧致格式不仅具有较高精度,还具有优于传统单点显式差分的高分辨率(保频谱性)。(3)把紧致格式改写成重构函数的形式(表达在网格单元中心上),同时给出了一种紧致重构函数的边界处理方法,稳定性分析表明,这些格式是渐进稳定的。(4)发展出了适用于双曲系统的紧致TVD格式以及特征型紧致TVD格式。(5)通过大量算例着重考察了特征型紧致TVD格式的精度,并与文献中的高阶格式进行了一些比较,发现本文格式具有精度高,虚假波动小,对流场细小结构的刻画能力强等优点。
本文还对格式精度、网格和CFD不确定度进行了简单考察。计算表明,若采用二阶格式,压力计算很容易达到两位真值准确,但是,除非网格极密,摩擦阻力很难达到两位真值准确。采用高阶格式可以提高计算结果的置信度,而且压力基本能达到三位真值准确。在摩阻和热流方面,计算达到两位真值准确是相对比较容易实现的,但是要想达到三位真值准确,高阶格式已经很难,低阶格式就更难。
在稳定性研究方面,本文采用抛物化稳定性方程(PSE)研究了二维超音速边界层的线性和非线性稳定性,并对PSE的特征值进行了分析,发现了一些文献中没有发现的现象,比如PSE的主特征值除了一个为v/u外,其余都为零。PSE的次特征与流向波数α有关。若α=0,则次特征为抛物-双曲型。若α的实部不为零,则必然会出现复特征值,即当扰动在流向存在波动性时,必定会在稳定性方程中导致椭圆性。若α的虚部的绝对值超过某个临界值,仍然可能在稳定性方程中导致椭圆性。根据参考文献,目前主要有两种方法可以克服PSE的椭圆性,一种是对压力扰动采取修正,另一种是采用较大的空间推进步长。
本文发展出了PSE的算法,采用PSE对Ma = 4.5的平板边界层的稳定性问题进行了研究,并用DNS验证了本文研究方法的正确性。通过与DNS和LST的比较,发现PSE的计算效率最高,而且计算精度基本与DNS相当。通过采用二维非线性PSE对边界层稳定性的研究,发现随着基本扰动的增大,会出现以下非线性现象:(1)稳定的高阶谐波会变得不稳定;(2)基频扰动幅值越大,失稳的高阶谐波越多,谐波的增长速度越快;(3)高阶谐波失稳的位置随着基频扰动幅值的增大而向上游移动;(4)高阶谐波增长有向饱和状态发展的趋势;(5)从涡量上看,大涡向小涡破碎,在临界层内的小涡更加丰富,大涡和小涡以及小涡和小涡之间相互作用,使得临界层内的涡量增长更快。本文发展出了三维PSE的算法,并采用三维线性PSE进行了稳定性研究,发现: (1)二维波可以自动调制出展向扰动,而且展向扰动的增长速度比其它扰动更快; (2)展向扰动呈现出两个极值点,一个在紧靠壁面的附近,另一个更大的极值点在临界层附近,临界层内的展向扰动等值线向前倾斜分布; (3)当采用数值方法进行稳定性分析时,网格密度应该与波矢方向上的波长相匹配。
本文最后还采用DNS方法研究了(1)激波-边界层相互作用对小扰动传播的影响和(2)法向速度扰动在2度攻角高超音速钝锥中的演化。一个斜激波被入射到Ma=4.5的平板边界层上,与边界层相互作用诱导分离等复杂流动结构,并对小扰动的传播存在非常大的影响。本文发现分离区不仅对扰动波具有抑制作用,同时,还会激发出新的低频扰动;在分离区内扰动呈现出第二模式的特征;激波和边界层加厚会使扰动波的传播速度变慢;激波与分离对扰动波的影响并不局限在激波两侧和分离区内,都存在着相应的影响区域。通过对2度攻角高超音速钝锥的稳定性计算发现,由于攻角的存在,钝锥的稳定性特征与零攻角时有本质的差别,比如背风面的扰动比迎风面增长更快,但扰增长最慢的地方并不是迎风面,而是侧面的某个位置;又比如背风面主要是长波起作用,迎风面和侧面主要是短波起作用;斜模式不稳定在整个钝锥边界层中起最主要的作用。
With the continuous development of aeronautic and astronautic technology, there are more and more supersonic and hypersonic aero/space crafts. The essential difference between laminar flow and turbulent flow causes large changes in aerodynamic force and heat as well as noise, which has vital effect on the performance and safety of the crafts. However, the achievements on supersonic/hypersonic boundary layer instability and laminar to turbulent transition are still limited. The study of the instability of supersonic/hypersonic flows is a tough task because of the following difficulties: it is very difficult to simulate this kind of flight environments in wind tunnels, and the experiment costs are expensive; direct numerical simulations (DNS) are restrained for the limitation of computing speed and RAM capability; theoretical studies about fluid instability were advancing very slowly for more than 100 years. The existence of shock waves in high-speed flows makes things much harder, such as shock-boundary interactions. Furthermore, small-structure shock waves may come into being during the instability process. Numerical algorithms should not only smoothly capture discontinuities, but also preserve favorable high-order accuracy in order to accurate simulating every trivial instability factors. A kind of nonoscillatory high-order shock-capturing finite difference schemes is formulated in this paper. Parabolized stability equations (PSE) and DNS are employed to study the instability of supersonic/hypersonic boundary layers.
The following works about high-order schemes have been done: (1) Works about TVD schemes including a new TVD criterion, TVD limiters, and a new method transforming linear schemes into TVD ones. Numerical tests show that this kind of TVD schemes can generally hold the high-order accuracy of their original linear schemes, and the limiters have no effect on resolution properties. (2) Linear compact schemes are reviewed. A class of compact schemes from 1st order to 7th order is given. The accuracy and resolution power of some high-order schemes are studied by Fourier analysis method. The results show that compact schemes possess the advantage of high-order accuracy and high resolution compared with the traditional schemes. (3) Compact schemes are converted into reconstruction forms (at cell center). Boundary closure is given for compact reconstruction functions. Stability analysis shows that the schemes are linearly stable. (4) Compact-TVD schemes and characteristic-based compact-TVD schemes are devised for hyperbolic systems. (5) The properties of the characteristic-based compact-TVD schemes are checked on some benchmark problems in one, two and three space dimensions. Our results are compared with those of other high-order schemes, and the results show that our schemes are high-order accurate with high resolution and less oscillatory.
The relations among CFD uncertainty, grid and numerical discrete accuracy are discussed. Our results indicate that pressure will easily reach two-digital virtual value accuracy even by lower order numerical schemes (2nd order). However, if the scheme is a 2nd order one, friction can hardly reach two-digital virtual value accuracy except that the grid is enough refined. High-order schemes (at less 3rd order) show advantages in improving the probability of accurate computing. If higher order schemes are used, pressure can even reach three-digital virtual value accuracy. Generally speaking, present numerical means can relatively easily reach two-digital virtual value accuracy, while three-digital virtual value accuracy is a tough goal for high-order schemes, and a much harder task for lower order schemes.
Linear and nonlinear stability of 2D supersonic boundary layers is studied using PSE. Characteristics analysis shows some special aspects which are ignored in literatures in the references. The main characteristics of PSE are zero except v/u. The second characteristics of PSE are related to the complex wave numberα. Ifαis zero, the PSE with their second characteristics are parabolic-hyperbolic. If the real part ofαis nonzero, two or more complex characteristics must appear. If the ABS of the image part ofαis greater than a critical number, a pair of conjugate complex number would appear in the second characteristics. There are mainly two ways to suppress the ellipticity of PSE: by modifying the pressure-gradient term of the pressure disturbance or by employing large marching steps.
The discretization formulas are given for PSE. PSE are employed to study the stability of a Ma = 4.5 planar plate boundary layer, and its correctness is confirmed by DNS. Compared with LST and DNS, linear and nonlinear PSE calculations yield results that are in good agreement with that of DNS, while the computational cost of PSE is the lowest among the three. The nonlinear PSE calculations show that the following nonlinear phenomena will emerge with every enhanced initial disturbance: (1) The stable harmonic waves will become unstable; (2) The larger the basic disturbance is, the more unstable harmonic waves there will be, and the faster the increasing speed of the unstable harmonic waves will become; (3) The critical positions where the harmonic waves become unstable are moving upwind with the increasing amplitude of the basic disturbance; (4) Harmonic waves are likely to reach a saturation state; (5) Large scale vortices will break down into small scale vortices, which makes the critical layer filled with abundant small scale vortices, and the mutually interaction of vortices results in that the vortices increase their amplitude more fast.
The algorithms for solving 3D PSE are developed. 3D linear PSE is applied to study the stability performance of a boundary layer. The results show that: (1) 2D waves will self-modulate a transverse disturbance, and the transverse disturbance increases faster than the 2D waves; (2) Two extreme points are found on the transverse disturbance, the smaller one is closer to the wall, while the larger one is in the critical layer; (3) When numerical methods are applied to study fluids instabilities, the grid size shall be allocated in according to the wavewise wavelength instead of the streamwise wavelength.
The stabilities of shock-boundary interaction and a hypersonic blunt cone at 2 degree angle of attack (AOA) are studied by DNS. An oblique shock wave is imposed on a two dimensional laminar Ma = 4.5 flow. A separation bubble forms between the shock wave and the solid plane, and the bubble causes compressing waves, expansion waves and a vortex. These complex flow structures have great influence on the stability. We find that the separation bubble can not only make the disturbance stable, but also modulate lower frequency waves. Second mode instability is found in the separation bubble. The travel speed of the disturbance is slowed down by the conjoint influence of the shock and the thickened boundary layer. The influence regions of the shock and the separation bubble are far more than the shock and the bubble themselves. Another DNS study is the evolutions of a vertical velocity disturbance in the boundary layer of the hypersonic cone at 2 degree AOA. The results show that the stability characters are quite different from cases without AOA. The leeward boundary is more unstable than the windward boundary. The most stable position is not in the windward, but in the sideward. The unstable waves in the leeward are mainly long waves, while the unstable waves in the windward and sideward are shorter ones. The main instability mechanism is an oblique model.
引文
[1] Bowles R I. Tranistion to Turbulent Flow in Aerodynamics[J]. The Royal Society, 2000, 358: 245-260.
[2]袁湘江,周恒.超声速边界层中小幅值T-S波的数值研究[J].应用数学和力学, 2000, 21(12): 1211-1214.
[3]瞿章华,曾明,刘伟等.高超声速空气动力学[M].国防科技大学出版社, 1999.
[4]童秉刚,孔详言,邓国华.气体动力学[M].高等教育出版社, 1989.
[5]张涵信,庄逢甘.与物理分析相结合的计算流体力学[A].新世纪力学研讨会——钱学森技术科学思想的回顾与展望论文集,国防工业出版社,北京,2001,128-143.
[6] Kroll N. ADIGMA - A European Project on the Development of Adaptive Higher Order Variational Methods for Aerospace Applications[A]. European Conference on Computational Fluid Dynamics, Eccomas CDF 2006.
[7] Harten A. Nonoscillatory Second-Order Accurate Shock-Capturing Schemes[A]. Methodes Numeriques De L?ngenieur, Comptes Rendus Du Troisieme Congres International[C]. Paris, Fr: Pluralis, Paris, Fr, 1983. 35-43.
[8] Harten A. High Resolution Schemes for Hypersonic Conservation Laws[J]. Journal of Computational Physics, 1983, 49: 357-393.
[9]张涵信.无波动、无自由参数的耗散差分格式[J].空气动力学学报, 1988, 6: 143-165.
[10] Osher S. Efficient Implementation of High Order Accurate Essentially Non-Oscillatory Shock Capturing Algorithms Applied to Compressible Flow[A]. Numerical Methods for Compressible Flows - Finite Difference, Element and Volume Techniques. Anaheim, Ca, UAS: ASME, New York, NY, UAS, 1986. 127-128.
[11] Harten A, Osher S. Uniformly High-Order Accurate Nonoscillatory Schemes[J]. SIAM Journal on Numerical Analysis, 1987, 24(2): 279-309.
[12] Chakravarthy S R, Harten A, Osher S. Essentially Non-Oscillatory Shock-Capturing Schemes of Arbitrarily-High Accuracy[A]. AIAA 24th Aerospace Sciences Meeting. Reno, Nv, UAS. AIAA, New York, NY, UAS, 1986. 14.
[13] Shu C W, Zang T A, Erlebacher G, et al. High-Order ENO Schemes Applied to Two- and Three-Dimensional Compressible Flow[J]. Applied Numerical Mathematics, 1992, 9(1): 45-71.
[14] Harten A, Osher S, Engquist B, et al. Uniformly High Order Essentially Non-Oscillatory Schemes II[J]. Journal of Computational Physics, 1987, 71: 231-303.
[15] Shu C W. Numerical Experiments on the Accuracy of ENO and Modified ENO Schemes[J]. Journal of Scientific Computing, 1990, 5(2): 127-149.
[16] Yang J Y. Third-Order Nonoscillatory Schemes for the Euler Equations[J]. AIAA Journal, 1991, 29(10): 1611-1618.
[17] Osher S, Shu C W. High-Order Essentially Nonoscillatory Schemes for Hamilton-Jacobian Equations[J]. SIAM Journal on Numerical Analysis, 1991, 28(4): 907-922.
[18] Zhong X. Application of Essentially Nonoscillatory Schemes to Unsteady Hypersonic Shock-Shock Interference Heating Problems[J]. AIAA Journal, 1994, 32(8): 1606-1616.
[19] Jiang G S, Shu C. Efficient Implementation of Weighted ENO Schemes[J]. Journal of Computational Physics, 1996, 126: 202-228.
[20] Liu X D, Osher S, Chan T. Weighted Essentially Non-Oscillatory Schemes[J]. Journal of Computational Physics, 1994, 115: 200-212.
[21] Shu C. Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws[R]. NASA/CR-97-206253, 1997.
[22] Liu M S, Sterren C J. A New Flux-Vector Splitting Scheme[J]. Journal of Computational Physics, 1993, 107: 23-29.
[23] Liou M S. A Sequel to AUSM: AUSM+[J]. Journal of Computational Physics, 1996, 129: 364-382.
[24] Kim K H, Lee J H, Rho O H. Improvement of AUSM Schemes By Introducing the Pressure-Based Weight Functions[J]. Computers & Fluids, 1998, 27(3): 311-346.
[25] Kim K H, Kim C, Rho O H. Accurate Computations of Hypersonic Flows Using AUSMPW+ Scheme and Shock-Aligned Grid Technique[R]. AIAA 98-2442, 1998.
[26] Alonso L, Martinelli L, Jameson A. Multigrid Unsteady Navier-Stokes Equations Calculations with Aeroelastic Applications[R]. AIAA 95-0049, 1995.
[27] Suresh A, Huynk H T. Accurate Monotonicity Perserving Scheme with Runge-Kutta Time Stepping[J]. Journal of Computational Physics, 1997, 136: 83-99.
[28] Daru V, Tenaud C. High Order One Step Monotonicity-Preserving Schemes for Unsteady Compressible Flow Calculations[J]. Journal of Computational Physics, 2004, 193(2): 563-594.
[29]张涵信,李沁,庄逢甘.关于建立高阶差分格式的问题[J].空气动力学学报, 1998, 16(1): 14-23.
[30]张涵信,贺国宏.高阶精度差分求解气动方程的几个问题[J].空气动力学学报, 1993, 11(4): 347-356.
[31]李沁,张涵信,高树椿.一种混合型四阶格式、基于特征的边界条件及其应用[J].空气动力学学报, 2000, 18(2): 146-155.
[32]宗文刚,邓小刚,张涵信.双重加权实质无波动激波捕捉格式[J].空气动力学学报, 2003, 21(2): 218-225.
[33]邓小刚.高阶精度耗散加权紧致非线性格式[J].中国科学A辑, 2001, 31(12): 1104-1117.
[34] Deng X, Zhang H. Developing High-Order Weighted Compact Nonlinear Schemes[J]. Journal of Computational Physics, 2000, 165: 22-44.
[35] Deng X, Maekawa H. Compact High-Order Accurate Nonlinear Schemes[J]. Journal of Computational Physics, 1997, 130: 77-91.
[36]刘昕.高阶精度加权紧致非线性格式研究与其在复杂流动中的应用[博士].四川绵阳:中国空气动力研究与发展中心研究生部, 2004.
[37]马延文,傅德薰.群速度直接控制四阶迎风紧致格式[J].中国科学A辑, 2001, 31(6): 554-561.
[38]高慧,马延文,傅德薰.六阶精度的群速度直接控制紧致格式及其应用[J].航空动力学报, 2003, 18(1): 197-207.
[39]李新亮,傅德薰,马延文. 8阶群速度控制格式及其应用[J].力学学报, 2004, 36(1): 79-83.
[40]田保林,傅德薰,马延文.群速度控制格式及二维Riemann解[J].计算力学学报, 2005, 22(1): 104-108.
[41]沈孟育,李海东,刘秋生.用解析离散法构造WENO-FCT格式[J].空气动力学学报, 1998, 16(1): 56-63.
[42]沈孟育,牛晓玲,张志斌.满足“抑制波动原则”的广义紧致格式的特性及应用[J].应用力学学报, 2003, 20(2): 12-16.
[43]沈孟育,张志斌,牛晓玲.满足抑制波动原则的五阶精度紧致格式[J].清华大学学报(自然科学版), 2002, 42(11): 1511-1514.
[44]沈孟育,蒋莉.满足熵增原则的高精度高分辨率格式[J].清华大学学报(自然科学版), 1999, 39(4): 1-5.
[45]李海东,任玉新,刘秋生等.高精度无波动激波捕捉方法[J].计算物理, 1996, 13(3): 277-273.
[46] Ren Y, Xu H. Shock Capturing Scheme Based on Two-Shock Approximation to Riemann Problem[J]. Qinghua Daxue Xuebao/Journal of Tsinghua University, 2001, 41(11): 15-18.
[47] Ren Y, Liu M, Zhang H. A Characteristic-Wise Hybrid Compact-WENO Schemes for Solving Hyperbolic Conservations[J]. Journal of Computational Physics, 2005, 192: 365-386.
[48] Liu W, Zhao H Y, Xie Y F. Construction of Third-Order WNND Scheme and Its Application in Complex Flow, Applied Mathematics and Mechanics (English Edition) 26 (1) (2005) 35-43.
[49] Yuan X, Zhou H. Numerical Schemes with High Order of Accuracy for the Computation of Shock Waves[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(5): 480-500.
[50] Shan P. Flux Vector Splitting Explicit Scheme and Simulation of 2-D Nozzle's Propulsive Jet[J]. Journal of Aerospace Power/Hangkong Dongli Xuebao, 1991, 6(1): 46-50.
[51]郑华盛,赵宁.一类高精度TVD差分格式及其应用[J].应用力学学报, 2005, 22(4): 550-554.
[52]徐振礼,刘儒勋,邱建贤.双曲守恒律方程的加权本质无振荡格式新进展[J].力学进展, 2004, 34(1): 9-22.
[53]王嘉松,倪汉根,何友声.双曲型线性方程三阶和四阶TVD格式的新构造[J].上海交通大学学报, 2003, 37(4): 549-552.
[54]李荫藩,宋松和,周铁.双曲型守恒律的高阶、高分辨有限体积法[J].力学进展, 2001, 31(2): 245-262.
[55] Hirsh R S. High Order Accurate Difference Solutions of Fluid Mechanics Problems By a Compact Differencing Technique[J]. Journal of Computational Physics, 1975, 19: 90-109.
[56] Lele S K. Compact Finite Difference Schemes with Spectral-Like Resolution[J]. Journal of Computational Physics, 1992, 103(1): 16-42.
[57] Fu D, Ma Y. Analysis of Super Compact Finite Difference Method and Application to Simulation of Vortex-Shock Interaction[J]. International Journal for Numerical Methods in Fluids, 2001, 36(7): 773-805.
[58] Adams N A, Shariff K. A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems[J]. Journal of Computational Physics, 1996, 127(1): 27.
[59] Tlstykh A I, Lipavskii M V. on Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing[J]. Journal of Computational Physics, 1998, 140: 205-232.
[60] Zhuang M, Cheng R F. Optimized Upwind Dispersion-Relation-Preserving Finite Difference Scheme for Computational Aeroacoustics[J]. AIAA Journal, 1998, 36(11): 2146-2148.
[61] Chu P C, Fan C. Sixth-Order Difference Scheme for Sigma Coordinate Ocean Models[J]. Journal of Physical Oceanography, 1997, 27(9): 2064-2071.
[62] Mahesh K. A Family of High Order Finite Difference Schemes with Good Spectral Resolution[J]. Journal of Computational Physics, 1998, 145: 332-358.
[63]沈孟育,牛晓玲.三点五阶优化广义紧致格式[J].空气动力学学报, 2003, 21(4): 384-391.
[64] Gaitonde D, Shang J S. Optimized Compact-Difference-Based Finite-Volume Schemes for Linear Wave Phenomena[J]. Journal of Computational Physics, 1997, 138: 617-643.
[65] Kobayashi M H. On A Class of PadéFinite Volume Methods[J]. Journal of Computational Physics, 1999, 156: 137-180.
[66] Sabau A S, Paad P E. Comparisons of Compact and Classical Finite Difference Solutions of Stiff Problems on Nonuniform Grids[J]. Computers & Fluids, 1999, 28(3): 361-384.
[67] Cockburn B, Shu C W. Nonlinearly Stable Compact Schemes for Shock Calculations[J]. SIAM Journal on Numerical Analysis, 1994, 31(3): 607-627.
[68]涂国华,罗俊荣.利用通量限制思想改进紧致格式[J].计算物理,2005,22(4): 329-336.
[69] Yee H C. Explicit and Implicit Multidimensional Compact High-Resolution Shock-Capturing Methods: Formulation[J]. Journal of Computational Physics, 1997, 131: 216-232.
[70] Ravichandran K S. Higher Order KFVS Algorithms Using Compact Upwind Difference Operators[J]. Journal of Computational Physics, 1997, 130: 161-173.
[71] Lerat A, Corre C. A Residual-Based Compact Schemes for the Compressible Navier-Stokes Equations[J]. Journal of Computational Physics, 2001, 170: 642-675.
[72]涂国华,袁湘江,陈陆军.适用于超声速的一种通量限制型紧致格式[J].航空学报, 2004, 25(4): 327-332.
[73]涂国华,袁湘江,夏治强等.一类TVD型的迎风紧致差分格式[J].应用数学和力学,2007, (6): 765-772.
[74] Wang Z, Huang G. an Essentially Nonoscillatory High-Order Padé-Type (ENO-Padé) Scheme[J]. Journal of Computational Physics, 2002, 177: 37-58.
[75] Pirozzoli S. Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction[J]. Journal of Computational Physics, 2002, 178(1): 81-117.
[76] Titarev V A, Collela P. Ader: Arbitrary High Order Godunov Approach[J]. Journal of Scientific Computing, 2002, 17(1-4): 609-618.
[77]张涵信,周恒.流体力学的基础研究[J].世界科技研究与发展, 2001, 23(1): 15-18.
[78] Janke E, Balakumar P. On the Stability of Three-Dimensional Boundary Layers, Part 1: Linear and Nonlinear Stability[R]. NASA/CR-1999-209330, ICASE Report No. 99-16, 1999.
[79] Orr M. The Stability or Instability of the Steady Motions of a Perfect Liquid and of Viscous Liquid[J]. Proc. Roy. Irish a Cad, 1907, 27: 9-138.
[80] Sommerfeld A. Ein Beitrag Zur Hydrodyna-Mischen Erkaerung Der Turbulenten Fluessigkei-Sbewegungen[A]. Proceedings 4th International Congress Mathematics[C]. Rome, 1908. Vol. III, p116-124.
[81] Tollmien W. Uber Die Entstehung Der Turbulenz. Nachr[J]. Ges. Wiss. Gottingen, Math-Phys., Kl. 1929. (21).
[82] Schlichting H. Zur Entstshung Turbulenz Bei Der Plattenstromung[J]. Nachr. Ges. Wocs. Gottingen[J]. Math-Phys[C], KL. 1933, P81-208.
[83] Schubauer G B, Skramstad H K. Laminar Boundary Layer Oscillations and Transition on a FlatPlate[J]. NACA Advanced Confidential Report 909, 1943.
[84] Liepmann H W. Investigation of Boundary Layer Transition on Concave Walls[R]. NACA wartime Rep. ACA 4328, 1945.
[85] Smith A M, Gamberoni N. Transition, Pressure Gradient and Stability Theory[R]. Report No. Es 26388, 1956.
[86] Van Ingen J L. A Suggested Semi-Empirical Method for the Calculation of the Boundary Layer Transition Region[R]. Report Uthl-74, University of Technoloty, Dept. Aero. Eng., 1956.
[87] Gaster M. On the Effects of Boundary Layer Growing on Flow Stability[J]. Journal of Fluid Mechanics, 1974, 66(3): 465-480
[88] Bouthier M. Stability Lineaire des Ecoulements Presque Paralleles[J]. J. Mecanique, 11.1972.
[89] Saric W S, Nayfeh A H. Nonparallel Stability of Boundary-Layer Flows[J]. Phys. Fluids, 1975, 18.
[90] Van Stijn T L, Vande Vooren A I. On the Stability of Almost Parallel Boundary Layer Flows[J]. Comp. Fluids, 1983, 10.
[91] Hall P. The Linear Development of Gortler Vortices in Growing Boundary Layers[J]. Journal of Fluid Mechanics. 1983 130: 103-180.
[92] Herbert T, Bertolotti F P. Stability Analysis of Nonparallel Boundary Layers[J]. J. Bull. Am. Phys. 1987. Soc. 32, p2079.
[93] Klebanoff P S, Tidstrom T D, Sargent L M. The Three-Dimensional Nature of Boundary Stability[J]. Journal of Fluid Mechanics, 1962, 12: 1-34.
[94] Craik A D D. Non-Linear Resonant Instability in Boundary Layers[J]. Journal of Fluid Mechanics, 1971, 50: 393-413.
[95] Herbert T. Subharmonic Three-Dimensional Disturbances in Unstable Plane Poiseuille Flows[R]. AIAA 83-1759, 1983.
[96] Herbert T. Analysis of Subharmonic Route to Transition in Boundary Layer[R]. AIAA 84-0009, 1984.
[97] Kachanov Y S, Levchenko V Y. The Resonant Interaction of Disturbances at Laminar-Turbulent Transition in Boundary Layer[J]. Journal of Fluid Mechanics, 1984, 138: 209-247.
[98] Kachanov Y S. on the Resonant Nature of the Breakdown of a Laminar Boundary Layer[J]. Journal of Fluid Mechanics, 1987, 184: 43-74.
[99]周恒,赵耕夫.流动稳定性[M].北京:国防工业出版社, 2004.
[100] Herbert T. Parabolized Stability Equations[J]. Annual Review of Fluid Mechanics, 1997, 29: 245-283.
[101] Chang C L, Malik M R. Oblique-Mode Breakdown and Secondary Instability in Supersonic Boundary Layers[J]. Journal of Fluid Mechanics, 1994, 273: 323-360.
[102] Herbert T. Boundary-Layer Transition - Analysis and Prediction Revisited[R]. AIAA 91-0737, 1991.
[103] Hu S, Zhong X. Nonparallel Stability Analysis of Compressible Boundary Layer Using 3-D PSE[R]. AIAA99-0813, 1999.
[104] Chang C L. The Langley Stability and Transition Analysis Code (LASTRAC): LST, Linear & Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers[R]. AIAA 2003-0974, 2003.
[105] Malik M R, Lin R S. Transition Predition on the Slat of a High-Lift System[J]. Journal of Aircraft, 2004, 41(6): 1384-1392.
[106] Galionis I, Hall P. Spatial Stability of the Incompressible Corner Flow[J]. Theoretical and Computational Fluid Dynamics, 2005, 19(2): 77-113.
[107] Hein S. Nonlinear Nonlocal Transition Analysis[J]. D L R - Forschungsberichte, 2005, (10): 145.
[108] Nomura T. PSE Analysis of Swept-Cylinder Boundary Layers Computed By Navier-Stokes Code[R]. AIAA2001-2703, 2001.
[109]董亚妮,周恒.二维超音速边界层中三波共振和二次失稳机制的数值模拟研究[J].应用数学和力学, 2006, 27(2): 127-133.
[110]曹伟,黄章峰,周恒.超音速平板边界层转捩中层流突变为湍流的机理研究[J].应用数学和力学, 2006, 27(4): 379-386.
[111]罗纪生,陆昌根,周恒.流动稳定性中小扰动波传播速度的数值研究[J].空气动力学学报, 2002, 20(1): 1-8.
[112]曹伟,周恒.二维高超音速边界层扰动演化的数值研究及小激波的存在对流场结构的影响[J].中国科学G辑, 2004, 34(2): 203-212.
[113]黄章峰,曹伟,周恒.超音速平板边界层转捩中层流突变为湍流的机理——时间模式[J].中国科学G辑,2005,35(5):537-547.
[114]王新军,罗纪生,周恒.平面槽道流中层流-湍流转捩的“Breakdown”过程的内在机理[J].中国科学G辑, 2005, 35(1): 71-78.
[115]张永明,周恒.抛物化稳定性方程在可压缩边界层中应用的检验[J].应用数学和力学, 2007, 28(8): 883-893.
[116]李明军,高智.流体运动稳定性方程组椭圆特性的分析与应用[J].应用数学和力学, 2003, 24(11): 1179-1185.
[117]李明军,高智.二维抛物化稳定性方程的特征和次特征[J].应用力学学报, 2002, 19(3): 124-126.
[118]郭琳琳,唐登斌,王伟志.带压力梯度的非平行流边界层稳定性研究[J].南京航空航天大学学报, 2005, 37(2): 169-173.
[119]夏浩,唐登斌,陆昌根.三维扰动波的非平行边界层稳定性研究[J].力学学报, 2002, 34(5): 688-695.
[120]郭乃龙.三维不可压边界层抛物化稳定性方程的椭圆特性研究[J].航空学报, 1999, 20(2): 104-106.
[121]夏浩,唐登斌,陆昌根.边界层流动的非平行稳定性研究[J].空气动力学学报, 2001, 19(2): 186-190.
[122] Roe P L. Approximate Riemann Solvers, Parameter Vectors and Difference Schemes[J]. Journal of Computational Physics, 1981, 43(2): 357-372.
[123] Casper J, Shu C W, Atkins H. Comparison of Two Formulations for High-Order Accurate Essentially Nonoscillatory Schemes[J]. AIAA Journal, 1994, 32(10): 1970-1977.
[124] Shu C W, Zeng Y. High-Order Essentially Non-Oscillatory Scheme for Viscoelasticity with Fading Memory[J]. Quarterly of Applied Mathematics, 1997, 55(3): 459-484.
[125] Osher S. Riemann Solvers, the Entropy Condition and Difference Approximations[J]. SIAM Journal on Numerical Analysis, 1984, 21(2): 217-238.
[126] Tadmor E. Convenient Total Variation Diminishing Conditions for Nonlinear Difference Schemes[J]. SIAM Journal on Numerical Analysis, 1988, 25(5): 1002-1014.
[127] Lee D. Multidimensional Supercompact Wavelets for Fluid Dynamics[J]. Numerical Heat Transfer, Part B: Fundamentals, 2003, 43(4): 307-329.
[128] Shen M Y, Zhang Z B, Niu X L. A New Way for Constructing High Accuracy Shock-Capturing Generalized Compact Difference Schemes[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(25): 2703-2725.
[129] Shen M Y, Niu X L, Zhang Z B. Three-Point Fifth-Order Accurate Generalized Compact Scheme and Its Applications[J]. Acta Mechanica Sinica/Lixue Xuebao, 2001, 17(2): 142-150.
[130] Shu C W, Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hypersonic Conservation Laws[A]. In Advanced Numerical Approximation of Nonlinear Hypersonic Equations, Springer-Verlag, Berlin, 1998, 1697: 425.
[131] Chakravarthy S R, Euler Equations--Implicit Schemes and Boundary Conditions[J]. AIAA Journal 1983, 21(5): 699-706.
[132] Tompson K W. Time Dependent Boundary Conditions for Hyperbolic Systems[J]. Journal of Computational Physics, 1987, 68: 1-24.
[133] Poinsot T, Lele S K. Boundary Conditions for Direct Simulations of Compressible Viscous Flows[J]. Journal of Computational Physics, 1992, 101: 104-129.
[134]张涵信,沈孟育.计算流体力学——差分方法的原理和应用[M].近代空气动力学丛书,国防工业出版社,北京,2003.1
[135] Shu C-W, Osher S. Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes[J]. Journal of Computational Physics, 1988(2), 77: 439-471.
[136] Shu C-W, Osher S. Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes II[J], Journal of Computational Physics, 1989, 83: 32-78.
[137] Zhang H-X, Zhuang F-G. NND Schemes and Their Applications to Numerical Simulation of Two- and Three-Dimensional Flows[J]. Advances in Applied Mechanics, 1992, 29 (193): 764-785.
[138] Schulz-Rinne C W. Classification of the Riemann Problem for Two-Dimensional Gas Dynamics[J]. SIAM J. Math. Anal., 1993, 24: 76-88.
[139] Schulz-Rinne C W, Collins J P, and Glaz H M. Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics[J]. SIAM J. Sci. Comput., 1993, 14 (6): 1394-1414.
[140] Lax P D, Liu X D. Solution of Two-Dimensional Riemann Problems of Gas Dynamics by PositiveSchemes[J]. SIAM J. Sci. Comput. 1998, 19 (2): 319–340.
[141] Levy D, Puppo G, Russo G. A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Law[J]. SIAM J. Sci. Comput. 2002, 24 (2): 480-506.
[142] Woodward P, Collela P. The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks[J]. Journal of Computational Physics, 1984, 54:115-173.
[143] Langseth J O, Leveque R J. A Wave Propagation Method for Three-Dimensional Hyperbolic Conservation Laws[J]. Journal of Computational Physics, 2000, 165: 126-166.
[144] Edney B. Anomalous Heat Transfer and Pressure Distributions on Blunt Bodies at Hypersonic Speeds in the Presence of an Impinging Shock[R]. FFA Report 115, Aero. Res. Inst. of Sweden, 1968.
[145] Wieting A R, Holden M S. Experimental Shock-Wave Interference Heating on a Cylinder at Mach 6 and 8[J]. AIAA Journal, 1989, 27 (11): 1557-1565.
[146] Thareja R R, Stewart J R. A Point Implicit Unstructured Grid Solver for the Euler and Navier-Stokes Equations[J]. International Journal for Numerical Methods in Fluids, 1989 9(4): 405-425.
[147] Zhong X. Application of High-Order Accurate Essentially Nonoscillatory Schemes to Two-Dimensional Compressible Viscous Flows[R]. AIAA Paper, AIAA-93-0879, 1993.
[148] Gustafsson B. The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems[J]. Math. Comput. 1975, 29(130): 396-406.
[149] Stetson K F, Thompson E R, Donaldson J C, and Siler L G. Laminar Boundary Layer Stability Experiments on a Cone at Mach 8, Part 2: Blunt Cone[R]. AIAA Paper 84-0006, January 1984.
[150] Stetson K F, Kimmel R L. On Hypersonic Boundary Layer Stability[R]. AIAA Paper 92-0797, 1992.
[151] Wendt V, Kreplin H P, H?hler G, Grosche F R, et al. Planar and Conical Boundary Layer Stability Experiments at Mach 5[R]. AIAA Paper 93-5112,1993.
[152] Lachowicz J T, Chokani N, Wilkinson S P. Hypersonic Boundary Layer Stability Over a Flared Cone in a Quiet Tunnel[R]. AIAA 96-0782, 1996.
[153] Doggett P G, Chokani N. Hypersonic Boundary-Layer Stability Experiments on a Flared-Cone Model at Angle of Attack in a Quiet Wind Tunnel[R]. AIAA 97-0577, 1997.
[154] Wilkinson S P. A Review of Hypersonic Boundary Layer Stability Experiments in a Quiet Mach 6 Wind Tunnel[R]. AIAA Paper, AIAA 97-1819, 1997.
[155] Schneider S P. Design and Fabrication of a 9.5-Inch Mach-6 Quiet-Flow Ludwieg Tube[R]. AIAA 98-2511.
[156] Schneider S P. Development of a Mach-6 Quiet-Flow Wind Tunnel for Transition[A]. Research in Laminar-Turbulent Transition: Proceedings of the 1999 Iutam Conference, Sedona. Springer-Verlag, 2000.
[157] Schneider S P Fabrication and Testing of the Purdue Mach-6 Quiet-Flow Ludweig Tube[R]. AIAA 2000-0295.
[158] Schneider S P. Flight Data for Boundary-Layer Transition at Hypersonic and Supersonic Speeds[J]. Journal of Spacecraft and Rockets. 1999, 36(1): 8-20.
[159] Beckwith I E. Development of a High Reynolds Number Quiet Tunnel for Transition Research[J] AIAA Journal, 1975, 13(3): 300-306.
[160] Martellucci A, Maguire B L, and Neff R S. Analysis of Flight Test Transition and Turbulent Heating Data, Part I: Boundary Layer Transition Results[R]. NASA CR-129045 (NASA Database Citation 73N12287), Nov. 1972.
[161] Berkowitz A M, Kyriss C L, and Martellucci A. Boundary Layer Transition Flight Test Observations[R]. AIAA Paper 77-125, Jan. 1977.
[162] Batt R G, Legner H H. A Review of Roughness-Induced Nosetip Transition[J]. AIAA Journal, 1983, 21(1): 7–22.
[163] Williamsonw E. Hypersonic Flight Testing[R]. AIAA Paper 92-3989, June 1992.
[164] Iliff Kw, Shafer M F. A Comparison of Hypersonic Flight and Prediction Results. AIAA Paper 93-0311, Jan. 1993.
[165] Malik M R. Instability and Tansition in Supersonic Boundary Layers[J]. Laminar Turbulent Boundary Layers, Fluids Engineering Div., American Society of Mechanical Engineers, 1984, 11: 139-147.
[166] Malik M R. Prediction and Control of Transition in Supersonic and Hypersonic Boundary Layers[J]. AIAA Journal, 1989, 27(11): 1487–1493.
[167] Murphy J D, Rubesin Mw. An Evaluation of Free-Flight Test Data for Aerodynamic Heating From Laminar, Turbulent, and Transitional Boundary Layers. Part II—The X-17 Re-Entry Body[R].NASA CR-70931.
[168] Balgeman E J, Cassell G, Dension M R, et. al. X-17 Re-Entry Test Vehicle: R-2 Final Flight Report[R]. Technical Rept. MSD-3003, Lockheed Aircraft Corp. (NASA Database Citation 74N78004), April 1957. (NASA Database Citation 66n20084), April 1965.
[169] Murphy J D, Rubesin M W. Re-Evaluation of Heat-Transfer Data Obtained in Flight Tests of Heat-Sink Shielded Re-Entry Vehicles[J]. Journal of Spacecraft, 1966, 3(1): 53-60.
[170] Wright R L, Zoby E V. Flight Boundary Layer Transition Measurements on a Slender Cone at Mach 20[R]. AIAA Paper 77-719, June 1977.
[171] Sherman M M, Nakamura T. Flight Test Measurements of Boundary Layer Transition on a Non-Ablating 22-Deg. Cone[R]. AIAA Paper 68-1152, Dec. 1968.
[172] Sherman M M, Nakamura T. Flight Test Measurements of Boundary Layer Transition on a Nonablating 22-Deg. Cone[J] Journal of Spacecraft and Rockets, 1970, 7(2): 137-142.
[173] Haigh W W, Lake B M, and Ko D R S. Analysis of Flight Data on Boundary Layer Transition at High Angles of Attack[R]. NASA CR-1913, April 1972.
[174] Johnson C B, Darden C M. Flight Transition Data for Angles of Attack at Mach 22 with Correlations of the Data[R]. NASA TM-X-3235 (NASA Database Citation 75N28377), Aug. 1975.
[175] Bouslog S A, An M Y. Hartmann L N, et al. Review of Boundary Layer Transition Flight Data on the Space Shuttle Orbiter[R]. AIAA Paper 91-0741, 1991.
[176] Rabb L, Disher J H. Boundary-Layer Transition at High Reynolds Numbers As Obtained in Flight of a 20-Deg. Cone-Cylinder with Wall to Local Stream Temperature Ratios Near 1.0[R]. NACA RM-E55I15 (NASA Database Citation 93R18171), Nov. 1955.
[177] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 10-Deg Cone in Free Flight at Supersonic Mach Numbers up to 5.9[R]. NASA TN-D-745 (NASA Database Citation 62N71319), May 1961; Supersedes NACA RM-L56b07.
[178] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 10-Deg. Cone in Free Flight at Supersonic Mach Numbers up to 5.9[R]. NACA RML56B07 (NASA Database Citation 93R18462), April 1956.
[179] Rabb L, Krasnican M J. Observation of Laminar Flow on an Air-Launched 15-Deg. Cone Cylinder at Local Reynolds Numbers to 50 Million at Peak Mach Number of 6.75[R]. NACA RM-E56l03 (NASA Database Citation 62N64173), March 1957.
[180] Rabb L, Krasnican M J. Effects of Surface Roughness and Extreme Cooling on Boundary-Layer Transition for a 15-Deg. Cone–Cylinder in Free Flight at Mach Numbers to 7.6[R]. NACA RM-E57K19 (NASA Database Citation 62N64606), March 1958.
[181] Garland B J, Swanson a G, Speegle K C. Aerodynamic Heating and Boundary-Layer Transition on a 1/10-Power Nose Shape in Free Flight at Mach Numbers up to 6.7 and Freestream Reynolds Numbers up to 16 Million[R]. NASA TN-D-1378 (NASA Database citation 62N13291), June 1962; Supersedes NACA RM L57E14A, 1957.
[182] Disher J H, Rabb L. Observation of Laminar Flow on a Blunted 15-Deg. Cone–Cylinder in Free Flight at High Reynolds Number and Free-Stream Mach Numbers to 8.17[R]. NACA RM- E56G23 (NASA Database Citation 62N63995), Oct. 1956.
[183] Krasnican M J, Rabb L. Effects of Nose Radius and Extreme Cooling on Boundary-Layer Transition for Three Smooth 15-Deg.-Cone-Cylinders in Free Flight at Mach Numbers to 8.50[R]. NASA Memo-3-4-59e (NASA Database Citation 63N14756), March 1959.
[184] Bond A C, Rumsey C B. Free-Flight Skin Temperature and Pressure Measurements on a Slightly Blunted 25-Deg. Cone–Cylinder–Flare Configuration to a Mach Number of 9.89[R]. NACA RM-L57b18 (NASA Database Citation 93R18905), April 1957.
[185] Buglia J J. Heat Transfer and Boundary-Layer Transition on a Highly Polished Hemisphere-Cone in Free Flight at Mach Numbers up to 3.14 and Reynolds Numbers up to 24 Times 10-6[R]. NASA TN-D-955, Sept. 1961; Supersedes NACA RM L57D05.
[186] Garland B J, Chauvin L T. Measurements of Heat Transfer and Boundary-Layer Transition on an 8-Inch-Diameter Hemisphere-Cylinde R in Free Flight for a Mach Number Range of 2.00 to 3.88[R]. NACARM-L57D04A, March 1957.
[187] Hall J R, Speegle K C, and Piland R O. Preliminary Results From a Free-Flight Investigation of Boundary-Layer Transition and Heat Transfer on a Highly Polished 8-Inch-Diameter Hemisphere-Cylinder at Mach Numbers up to 3 and Reynolds Numbers Based on a Length of 1 Foot up to 17.7 Million[R]. NACA RM L57D18C (NASA Database Citation 93R19061), May 1957.
[188] Chauvin L T, Speegle K C. Boundary-Layer-Transition and Heat-Transfer Measurements From 179Flight Tests of Blunt and Sharp 50-Deg. Cones at Mach Numbers From 1.7 to 4.7[R]. NACA RM-L57D04 (NASA Database Citation 66N33310), April 1957.
[189] Sternberg J. A Free-Flight Investigation of the Possibility of High Reynolds Number Supersonic Laminar Boundary Layers[J]. Journal of the Aeronautical Sciences, 1952, 19(11): 721-733.
[190] Merlet C F, Rumsey C B. Supersonic Free-Flight Measurement of Heat Transfer and Transition on a 10-Deg Cone Having a Low Temperature Ratio[R]. NASA TN-D-951 (NASA Database Citation 62N71525), Aug. 1961; Supersedes NACA RM L56l10, 1956.
[191] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer on a 15-Deg Cone–Cylinder–Flare Configuration in Free Flight at Mach Numbers up to 4.7[R]. NASA TN-D-824 (NASA Database Citation 62N71398), May 1961; Supersedes NACA RM L57J10, 1958.
[192] Rabb L, Simpkinson S. Free-Flight Heat-Transfer Measurements on Two 20-Deg- Cone-Cylinders at Mach Numbers From 1.3 to 4.9[R]. NACA RM-E55F27 (NASA Database Citation 62N63397), July 1955.
[193] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 15-Deg Cone in Free Flight at Supersonic Mach Numbers up to 5.2[R]. NASA TN-D-888 (NASA Database Citation 62N71462), Aug. 1961; Supersedes NACA RM L56F26, 1956.
[194] Braslow A L. Analysis of Boundary-Layer Transition on X-15-2 Research Airplane[R]. NASA TN-D-3487 (NASA Database Citation 66N30177), March 1966.
[195] Banner R D, Kuhl A E, and Quinn R D. Preliminary Results of Aerodynamic Heating Studies on the X-15 Airplane[R]. NASA TM-X-638, Jan. 1968.
[196] Gord P R. Measured and Calculated Structural Temperature Data From Two X-15 Airplane Flights with Extreme Aerodynamic Heating Conditions[R]. NASA TM-X-1358 (NASA Database Citation 74N71363), March 1967.
[197] Banner R D, Mctigue J G, and Petty G. Boundary-Layer-Transition Measurements in Full-Scale Flight[R]. NASA TM-79863 (NASA Database Citation 78N78570), Oct. 1978; Rev. NACA RM H58E28, July 1958.
[198] Fisher, D. F., and Dougherty, N. S.,“In-Flight Transition Measurement on a 10-Deg. Cone Atmach Numbers From0.5 to 2.0[R]. NASA TP-1971, 1982.
[199] Dougherty N S, Fisher D F. Boundary Layer Transition on a 10-Degree Cone: Wind Tunnel/ Flight Data Correlation[R]. AIAA Paper 80-0154, Jan. 1980.
[200] Quinn R D, Gong L. In-Flight Measurements on a Hollow Cylinder at a Mach Number of 3.0[R]. NASA TP-1764, Nov. 1980.
[201] Reed H, Saric W, Lyttle L, and Asada Y. Stability and Control of High-Speed Flows[R]. AIAA-2001-2700, 2001.
[202] Sugiura H,Tokugawa N, Ueda Y. Boundary-Layer Transition on an Axisymmetric Body at Incidence at Mach 1.2[J]. AIAA Journal 2006.5 44(5): 973-980.
[203] Ciolkosz L D, Spina E F. An Experimental Study of Gortler Vortices in Compressible Flow[A]. Collection of Technical Papers - AIAA/ASME/SAE/ASEE 42nd Joint Propulsion Conference, 2007, v3 p2036-2045.
[204] Zhong X, Ma Y. Receptivity and Linear Stability of Stetson's Mach 8 Blunt Cone Stability Experiments[R]. AIAA Paper, AIAA 2002-2849, 2002.
[205] Zhong X L, Tatineni M. Stable High-Order schemes and DNS of Boundary-Layer Stability on a Blunt Cone at Mach 8[R]. AIAA Paper, 2001-0437, 2001.
[206] Johnson H B, Seipp T G, and Candler G V. Numerical Study of Hypersonic Reacting Boundary Layer Transition on Cones[J]. Physics of Fluids, 1998 10(10): 2676-2685.
[207] Balakumar P. Stability of Supersonic Boundary Layers Over Blunt Wedges[A]. 36th AIAA Fluid Dynamics Conference Collection of Technical Papers - 36th AIAA Fluid Dynamics Conference,Jun, 2006, p487-496.
[208] Landau L D. On the problem of Turbulence. A kadem Iaa Nuuk SSSR. Dokaldy 1944, 44: 311-314.
[209] Stuart J T. On the Nonlinear Mechanics of Wave Disturbances in Stable and Unstable Parallel Flows, Part I: the Basic Behavior in Plane Poiseuille Flow[J]. Journal of Fluids Dynamics, 1960, (9): 353-370.
[210] Reshotko E. Boundary Layer Instability, Transition, and Control[R]. AIAA Paper 94-0001, Jan. 1994.
[211] Arnal D, Casalis G. Laminar-Turbulent Transition Prediction in Three-Dimensional Flows Progress in Aerospace Sciences, 2000, (36): 173-191.
[212] Reshotko E. Transition Issues at Hypersonic Speeds. Collection of Technical Papers[A]. 44th AIAA 180Aerospace Sciences Meeting, v12 p8472-8480, Jan, 2006.
[213] Reshotko E. Transition Issues for Atmospheric Entry[R]. 45th AIAA Aerospace Sciences Meeting and Exhibit, 8 - 11 January 2007, AIAA 2007-0304.
[214]傅德薰,马延文.平面混合流拟序结构的直接数值模拟.中国科学A辑,1996,26(7):659-664.
[215]曹伟.二维超音速混合层增强混合的研究[博士].天津大学,2001.
[216]赵耕夫.可压缩平板边界层的二次亚谐不稳定性[J].天津大学学报,2003, 36(3):276-280.
[217]苏彩虹,周恒.零攻角小钝头钝锥高超音速绕流边界层的稳定性分析和转捩预报[J].应用数学和力学, 2007, 28(5): 505-513.
[218]李新亮,,傅德薰,马延文.可压缩钝楔边界层转捩到湍流的直接数值模拟[J].中国科学G辑, 2004, 34(4): 466-480.
[219]刘嘉,雷麦芳,姚文秀,王发民.高超声速边界层流动转捩研究[J].计算物理, 2004, 21(1): 61-67.
[220]王发民,蔡春培,赵烈等.可压缩流动转捩的迭代求解[J].空气动力学学报, 1998, 16(4): 485-491.
[221]郭辉,连淇祥, Kachanov Y S, and Borodulin V I.边界层转捩过程三维扰动的发展和演化[J].北京航空航天大学学报, 2003, 29(6): 501-504.
[222] Ma Y, Fu D. Fourth Order Accurate Compact Scheme with Group Velocity Control (GVC)[J]. Science in China, Series A: Mathematics, Physics, Astronomy, 2001, 44(9): 1197-1204.
[223] Lynbimov A N, Ruasnov V V. Gas Flow Past Blunt Bodies[R]. NASA-TT-F715, 1973.
[224] Fay J A, Riddell R F. Theory of Stagnation Point Heat Transfer in Dissociated Air[J]. Journal of Aeronautical Sciences, 1958, 25: 73-85.
[225]张涵信,国义军.垂直于物面的横截面上流态的拓扑[J].空气动力学学报,2000, 18(1): 1-13.
[226] AIAA. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations[R]. AIAA G-007-1998 Reston, VA, 1998.
[227] Oberkampf W L, Trucano T G. Verification and Validation in Computational Fluid Dynamics[J]. Progress in Aerospace Sciences, 2002, 38: 209-272.
[228]侯中喜,夏刚,王承尧. CFD解的数值可靠性分析[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p790-795.
[229]邓小刚,宗文刚,张来平等.计算流体力学中的验证与确认[J].力学进展, 2007, 37(2): 279-288.
[230]于沛. CFD软件的算例验证确认技术[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p786-789.
[231]张涵信.航空航天工程中CFD的现状、面临的问题和发展[A].香山科学会议,第308次会议,航空航天工程应用中的湍流与CFD研究——现状、问题与发展对策.2007.9.
[232]恽起麟.风洞实验[M].近代空气动力学丛书.国防工业出版社.北京, 2000年9月.
[233]程厚梅等.风洞实验干扰与修正[M].近代空气动力学丛书.国防工业出版社.北京, 2003.1.
[234] Laflin K.R et al. Summary of Data From the Second AIAA CFD Dreg Prediction Workshop (Invited) [R]. AIAA 2004-0555.
[235] Tinoco E. N. Su T Y. Drag Prediction with the ZEUS/CFL3D System[R]. AIAA 2004-0552.
[236]张涵信,呙超,宗文刚.网格与高精度差分计算问题[J].力学学报,1999, 31(4): 398-405.
[237]张涵信,李沁.关于CFD数值解中网格、算法的协调问题[R].北京航空航天大学国际计算流体力学实验室交流报告,北京, 2007.
[238] AIAA. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations[R]. AIAA G-007-1998 Reston, VA, 1998.
[239] Oberkampf W L, Trucano T G. Verification and Validation in Computational Fluid Dynamics[J]. Progress in Aerospace Sciences, 2002, 38: 209-272.
[240]侯中喜,夏刚,王承尧. CFD解的数值可靠性分析[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p790-795.
[241]白文.气动计算软件可信度分析解决方案[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p770-774.
[242]于沛. CFD软件的算例验证确认技术[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p786-789.
[243]张涵信.航空航天工程中CFD的现状、面临的问题和发展[A].香山科学会议,第308次会议,航空航天工程应用中的湍流与CFD研究——现状、问题与发展对策. 2007.9.
[244] Haj-Hariri H. Characteristics Analysis of the Parabolized Stability Equations[J]. Studies in Appl Math, 1994 , 92 (1) : 41-53.
[245] Li F, Malik M R. Spectral Analysis of Parabolized Stability Equations [J]. Computer & Fluids, 26(3): 279-297, 1997.
[246] Th. Herbert. On Finite Amplitudes in Boundary Layers[R]. ESA, TT-169, 1975.
[247] Pagella A, Rist U, and Wagner S. Numerical Investigations of Small-Amplitude Disturbances in a Laminar Boundary Layer with Impinging Shock Wave at Ma=4.8[J]. Physics of Fluid, 2002, 14(7): 2088-2101.
[248]袁湘江,周恒.考虑流向曲率和压力梯度的可压缩边界层稳定性分析[J].空气动力学学报,1998, 16(3): 276-281.
[249]张涵信.关于CFD验证确认中几个概念和计算结果的不确定度问题.空气动力学学报,(待发)
[250] Anderson J D. Hypersonic and high-temperature gas dynamics[M]. AIAA, 2006
[2]袁湘江,周恒.超声速边界层中小幅值T-S波的数值研究[J].应用数学和力学, 2000, 21(12): 1211-1214.
[3]瞿章华,曾明,刘伟等.高超声速空气动力学[M].国防科技大学出版社, 1999.
[4]童秉刚,孔详言,邓国华.气体动力学[M].高等教育出版社, 1989.
[5]张涵信,庄逢甘.与物理分析相结合的计算流体力学[A].新世纪力学研讨会——钱学森技术科学思想的回顾与展望论文集,国防工业出版社,北京,2001,128-143.
[6] Kroll N. ADIGMA - A European Project on the Development of Adaptive Higher Order Variational Methods for Aerospace Applications[A]. European Conference on Computational Fluid Dynamics, Eccomas CDF 2006.
[7] Harten A. Nonoscillatory Second-Order Accurate Shock-Capturing Schemes[A]. Methodes Numeriques De L?ngenieur, Comptes Rendus Du Troisieme Congres International[C]. Paris, Fr: Pluralis, Paris, Fr, 1983. 35-43.
[8] Harten A. High Resolution Schemes for Hypersonic Conservation Laws[J]. Journal of Computational Physics, 1983, 49: 357-393.
[9]张涵信.无波动、无自由参数的耗散差分格式[J].空气动力学学报, 1988, 6: 143-165.
[10] Osher S. Efficient Implementation of High Order Accurate Essentially Non-Oscillatory Shock Capturing Algorithms Applied to Compressible Flow[A]. Numerical Methods for Compressible Flows - Finite Difference, Element and Volume Techniques. Anaheim, Ca, UAS: ASME, New York, NY, UAS, 1986. 127-128.
[11] Harten A, Osher S. Uniformly High-Order Accurate Nonoscillatory Schemes[J]. SIAM Journal on Numerical Analysis, 1987, 24(2): 279-309.
[12] Chakravarthy S R, Harten A, Osher S. Essentially Non-Oscillatory Shock-Capturing Schemes of Arbitrarily-High Accuracy[A]. AIAA 24th Aerospace Sciences Meeting. Reno, Nv, UAS. AIAA, New York, NY, UAS, 1986. 14.
[13] Shu C W, Zang T A, Erlebacher G, et al. High-Order ENO Schemes Applied to Two- and Three-Dimensional Compressible Flow[J]. Applied Numerical Mathematics, 1992, 9(1): 45-71.
[14] Harten A, Osher S, Engquist B, et al. Uniformly High Order Essentially Non-Oscillatory Schemes II[J]. Journal of Computational Physics, 1987, 71: 231-303.
[15] Shu C W. Numerical Experiments on the Accuracy of ENO and Modified ENO Schemes[J]. Journal of Scientific Computing, 1990, 5(2): 127-149.
[16] Yang J Y. Third-Order Nonoscillatory Schemes for the Euler Equations[J]. AIAA Journal, 1991, 29(10): 1611-1618.
[17] Osher S, Shu C W. High-Order Essentially Nonoscillatory Schemes for Hamilton-Jacobian Equations[J]. SIAM Journal on Numerical Analysis, 1991, 28(4): 907-922.
[18] Zhong X. Application of Essentially Nonoscillatory Schemes to Unsteady Hypersonic Shock-Shock Interference Heating Problems[J]. AIAA Journal, 1994, 32(8): 1606-1616.
[19] Jiang G S, Shu C. Efficient Implementation of Weighted ENO Schemes[J]. Journal of Computational Physics, 1996, 126: 202-228.
[20] Liu X D, Osher S, Chan T. Weighted Essentially Non-Oscillatory Schemes[J]. Journal of Computational Physics, 1994, 115: 200-212.
[21] Shu C. Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws[R]. NASA/CR-97-206253, 1997.
[22] Liu M S, Sterren C J. A New Flux-Vector Splitting Scheme[J]. Journal of Computational Physics, 1993, 107: 23-29.
[23] Liou M S. A Sequel to AUSM: AUSM+[J]. Journal of Computational Physics, 1996, 129: 364-382.
[24] Kim K H, Lee J H, Rho O H. Improvement of AUSM Schemes By Introducing the Pressure-Based Weight Functions[J]. Computers & Fluids, 1998, 27(3): 311-346.
[25] Kim K H, Kim C, Rho O H. Accurate Computations of Hypersonic Flows Using AUSMPW+ Scheme and Shock-Aligned Grid Technique[R]. AIAA 98-2442, 1998.
[26] Alonso L, Martinelli L, Jameson A. Multigrid Unsteady Navier-Stokes Equations Calculations with Aeroelastic Applications[R]. AIAA 95-0049, 1995.
[27] Suresh A, Huynk H T. Accurate Monotonicity Perserving Scheme with Runge-Kutta Time Stepping[J]. Journal of Computational Physics, 1997, 136: 83-99.
[28] Daru V, Tenaud C. High Order One Step Monotonicity-Preserving Schemes for Unsteady Compressible Flow Calculations[J]. Journal of Computational Physics, 2004, 193(2): 563-594.
[29]张涵信,李沁,庄逢甘.关于建立高阶差分格式的问题[J].空气动力学学报, 1998, 16(1): 14-23.
[30]张涵信,贺国宏.高阶精度差分求解气动方程的几个问题[J].空气动力学学报, 1993, 11(4): 347-356.
[31]李沁,张涵信,高树椿.一种混合型四阶格式、基于特征的边界条件及其应用[J].空气动力学学报, 2000, 18(2): 146-155.
[32]宗文刚,邓小刚,张涵信.双重加权实质无波动激波捕捉格式[J].空气动力学学报, 2003, 21(2): 218-225.
[33]邓小刚.高阶精度耗散加权紧致非线性格式[J].中国科学A辑, 2001, 31(12): 1104-1117.
[34] Deng X, Zhang H. Developing High-Order Weighted Compact Nonlinear Schemes[J]. Journal of Computational Physics, 2000, 165: 22-44.
[35] Deng X, Maekawa H. Compact High-Order Accurate Nonlinear Schemes[J]. Journal of Computational Physics, 1997, 130: 77-91.
[36]刘昕.高阶精度加权紧致非线性格式研究与其在复杂流动中的应用[博士].四川绵阳:中国空气动力研究与发展中心研究生部, 2004.
[37]马延文,傅德薰.群速度直接控制四阶迎风紧致格式[J].中国科学A辑, 2001, 31(6): 554-561.
[38]高慧,马延文,傅德薰.六阶精度的群速度直接控制紧致格式及其应用[J].航空动力学报, 2003, 18(1): 197-207.
[39]李新亮,傅德薰,马延文. 8阶群速度控制格式及其应用[J].力学学报, 2004, 36(1): 79-83.
[40]田保林,傅德薰,马延文.群速度控制格式及二维Riemann解[J].计算力学学报, 2005, 22(1): 104-108.
[41]沈孟育,李海东,刘秋生.用解析离散法构造WENO-FCT格式[J].空气动力学学报, 1998, 16(1): 56-63.
[42]沈孟育,牛晓玲,张志斌.满足“抑制波动原则”的广义紧致格式的特性及应用[J].应用力学学报, 2003, 20(2): 12-16.
[43]沈孟育,张志斌,牛晓玲.满足抑制波动原则的五阶精度紧致格式[J].清华大学学报(自然科学版), 2002, 42(11): 1511-1514.
[44]沈孟育,蒋莉.满足熵增原则的高精度高分辨率格式[J].清华大学学报(自然科学版), 1999, 39(4): 1-5.
[45]李海东,任玉新,刘秋生等.高精度无波动激波捕捉方法[J].计算物理, 1996, 13(3): 277-273.
[46] Ren Y, Xu H. Shock Capturing Scheme Based on Two-Shock Approximation to Riemann Problem[J]. Qinghua Daxue Xuebao/Journal of Tsinghua University, 2001, 41(11): 15-18.
[47] Ren Y, Liu M, Zhang H. A Characteristic-Wise Hybrid Compact-WENO Schemes for Solving Hyperbolic Conservations[J]. Journal of Computational Physics, 2005, 192: 365-386.
[48] Liu W, Zhao H Y, Xie Y F. Construction of Third-Order WNND Scheme and Its Application in Complex Flow, Applied Mathematics and Mechanics (English Edition) 26 (1) (2005) 35-43.
[49] Yuan X, Zhou H. Numerical Schemes with High Order of Accuracy for the Computation of Shock Waves[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(5): 480-500.
[50] Shan P. Flux Vector Splitting Explicit Scheme and Simulation of 2-D Nozzle's Propulsive Jet[J]. Journal of Aerospace Power/Hangkong Dongli Xuebao, 1991, 6(1): 46-50.
[51]郑华盛,赵宁.一类高精度TVD差分格式及其应用[J].应用力学学报, 2005, 22(4): 550-554.
[52]徐振礼,刘儒勋,邱建贤.双曲守恒律方程的加权本质无振荡格式新进展[J].力学进展, 2004, 34(1): 9-22.
[53]王嘉松,倪汉根,何友声.双曲型线性方程三阶和四阶TVD格式的新构造[J].上海交通大学学报, 2003, 37(4): 549-552.
[54]李荫藩,宋松和,周铁.双曲型守恒律的高阶、高分辨有限体积法[J].力学进展, 2001, 31(2): 245-262.
[55] Hirsh R S. High Order Accurate Difference Solutions of Fluid Mechanics Problems By a Compact Differencing Technique[J]. Journal of Computational Physics, 1975, 19: 90-109.
[56] Lele S K. Compact Finite Difference Schemes with Spectral-Like Resolution[J]. Journal of Computational Physics, 1992, 103(1): 16-42.
[57] Fu D, Ma Y. Analysis of Super Compact Finite Difference Method and Application to Simulation of Vortex-Shock Interaction[J]. International Journal for Numerical Methods in Fluids, 2001, 36(7): 773-805.
[58] Adams N A, Shariff K. A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems[J]. Journal of Computational Physics, 1996, 127(1): 27.
[59] Tlstykh A I, Lipavskii M V. on Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing[J]. Journal of Computational Physics, 1998, 140: 205-232.
[60] Zhuang M, Cheng R F. Optimized Upwind Dispersion-Relation-Preserving Finite Difference Scheme for Computational Aeroacoustics[J]. AIAA Journal, 1998, 36(11): 2146-2148.
[61] Chu P C, Fan C. Sixth-Order Difference Scheme for Sigma Coordinate Ocean Models[J]. Journal of Physical Oceanography, 1997, 27(9): 2064-2071.
[62] Mahesh K. A Family of High Order Finite Difference Schemes with Good Spectral Resolution[J]. Journal of Computational Physics, 1998, 145: 332-358.
[63]沈孟育,牛晓玲.三点五阶优化广义紧致格式[J].空气动力学学报, 2003, 21(4): 384-391.
[64] Gaitonde D, Shang J S. Optimized Compact-Difference-Based Finite-Volume Schemes for Linear Wave Phenomena[J]. Journal of Computational Physics, 1997, 138: 617-643.
[65] Kobayashi M H. On A Class of PadéFinite Volume Methods[J]. Journal of Computational Physics, 1999, 156: 137-180.
[66] Sabau A S, Paad P E. Comparisons of Compact and Classical Finite Difference Solutions of Stiff Problems on Nonuniform Grids[J]. Computers & Fluids, 1999, 28(3): 361-384.
[67] Cockburn B, Shu C W. Nonlinearly Stable Compact Schemes for Shock Calculations[J]. SIAM Journal on Numerical Analysis, 1994, 31(3): 607-627.
[68]涂国华,罗俊荣.利用通量限制思想改进紧致格式[J].计算物理,2005,22(4): 329-336.
[69] Yee H C. Explicit and Implicit Multidimensional Compact High-Resolution Shock-Capturing Methods: Formulation[J]. Journal of Computational Physics, 1997, 131: 216-232.
[70] Ravichandran K S. Higher Order KFVS Algorithms Using Compact Upwind Difference Operators[J]. Journal of Computational Physics, 1997, 130: 161-173.
[71] Lerat A, Corre C. A Residual-Based Compact Schemes for the Compressible Navier-Stokes Equations[J]. Journal of Computational Physics, 2001, 170: 642-675.
[72]涂国华,袁湘江,陈陆军.适用于超声速的一种通量限制型紧致格式[J].航空学报, 2004, 25(4): 327-332.
[73]涂国华,袁湘江,夏治强等.一类TVD型的迎风紧致差分格式[J].应用数学和力学,2007, (6): 765-772.
[74] Wang Z, Huang G. an Essentially Nonoscillatory High-Order Padé-Type (ENO-Padé) Scheme[J]. Journal of Computational Physics, 2002, 177: 37-58.
[75] Pirozzoli S. Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction[J]. Journal of Computational Physics, 2002, 178(1): 81-117.
[76] Titarev V A, Collela P. Ader: Arbitrary High Order Godunov Approach[J]. Journal of Scientific Computing, 2002, 17(1-4): 609-618.
[77]张涵信,周恒.流体力学的基础研究[J].世界科技研究与发展, 2001, 23(1): 15-18.
[78] Janke E, Balakumar P. On the Stability of Three-Dimensional Boundary Layers, Part 1: Linear and Nonlinear Stability[R]. NASA/CR-1999-209330, ICASE Report No. 99-16, 1999.
[79] Orr M. The Stability or Instability of the Steady Motions of a Perfect Liquid and of Viscous Liquid[J]. Proc. Roy. Irish a Cad, 1907, 27: 9-138.
[80] Sommerfeld A. Ein Beitrag Zur Hydrodyna-Mischen Erkaerung Der Turbulenten Fluessigkei-Sbewegungen[A]. Proceedings 4th International Congress Mathematics[C]. Rome, 1908. Vol. III, p116-124.
[81] Tollmien W. Uber Die Entstehung Der Turbulenz. Nachr[J]. Ges. Wiss. Gottingen, Math-Phys., Kl. 1929. (21).
[82] Schlichting H. Zur Entstshung Turbulenz Bei Der Plattenstromung[J]. Nachr. Ges. Wocs. Gottingen[J]. Math-Phys[C], KL. 1933, P81-208.
[83] Schubauer G B, Skramstad H K. Laminar Boundary Layer Oscillations and Transition on a FlatPlate[J]. NACA Advanced Confidential Report 909, 1943.
[84] Liepmann H W. Investigation of Boundary Layer Transition on Concave Walls[R]. NACA wartime Rep. ACA 4328, 1945.
[85] Smith A M, Gamberoni N. Transition, Pressure Gradient and Stability Theory[R]. Report No. Es 26388, 1956.
[86] Van Ingen J L. A Suggested Semi-Empirical Method for the Calculation of the Boundary Layer Transition Region[R]. Report Uthl-74, University of Technoloty, Dept. Aero. Eng., 1956.
[87] Gaster M. On the Effects of Boundary Layer Growing on Flow Stability[J]. Journal of Fluid Mechanics, 1974, 66(3): 465-480
[88] Bouthier M. Stability Lineaire des Ecoulements Presque Paralleles[J]. J. Mecanique, 11.1972.
[89] Saric W S, Nayfeh A H. Nonparallel Stability of Boundary-Layer Flows[J]. Phys. Fluids, 1975, 18.
[90] Van Stijn T L, Vande Vooren A I. On the Stability of Almost Parallel Boundary Layer Flows[J]. Comp. Fluids, 1983, 10.
[91] Hall P. The Linear Development of Gortler Vortices in Growing Boundary Layers[J]. Journal of Fluid Mechanics. 1983 130: 103-180.
[92] Herbert T, Bertolotti F P. Stability Analysis of Nonparallel Boundary Layers[J]. J. Bull. Am. Phys. 1987. Soc. 32, p2079.
[93] Klebanoff P S, Tidstrom T D, Sargent L M. The Three-Dimensional Nature of Boundary Stability[J]. Journal of Fluid Mechanics, 1962, 12: 1-34.
[94] Craik A D D. Non-Linear Resonant Instability in Boundary Layers[J]. Journal of Fluid Mechanics, 1971, 50: 393-413.
[95] Herbert T. Subharmonic Three-Dimensional Disturbances in Unstable Plane Poiseuille Flows[R]. AIAA 83-1759, 1983.
[96] Herbert T. Analysis of Subharmonic Route to Transition in Boundary Layer[R]. AIAA 84-0009, 1984.
[97] Kachanov Y S, Levchenko V Y. The Resonant Interaction of Disturbances at Laminar-Turbulent Transition in Boundary Layer[J]. Journal of Fluid Mechanics, 1984, 138: 209-247.
[98] Kachanov Y S. on the Resonant Nature of the Breakdown of a Laminar Boundary Layer[J]. Journal of Fluid Mechanics, 1987, 184: 43-74.
[99]周恒,赵耕夫.流动稳定性[M].北京:国防工业出版社, 2004.
[100] Herbert T. Parabolized Stability Equations[J]. Annual Review of Fluid Mechanics, 1997, 29: 245-283.
[101] Chang C L, Malik M R. Oblique-Mode Breakdown and Secondary Instability in Supersonic Boundary Layers[J]. Journal of Fluid Mechanics, 1994, 273: 323-360.
[102] Herbert T. Boundary-Layer Transition - Analysis and Prediction Revisited[R]. AIAA 91-0737, 1991.
[103] Hu S, Zhong X. Nonparallel Stability Analysis of Compressible Boundary Layer Using 3-D PSE[R]. AIAA99-0813, 1999.
[104] Chang C L. The Langley Stability and Transition Analysis Code (LASTRAC): LST, Linear & Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers[R]. AIAA 2003-0974, 2003.
[105] Malik M R, Lin R S. Transition Predition on the Slat of a High-Lift System[J]. Journal of Aircraft, 2004, 41(6): 1384-1392.
[106] Galionis I, Hall P. Spatial Stability of the Incompressible Corner Flow[J]. Theoretical and Computational Fluid Dynamics, 2005, 19(2): 77-113.
[107] Hein S. Nonlinear Nonlocal Transition Analysis[J]. D L R - Forschungsberichte, 2005, (10): 145.
[108] Nomura T. PSE Analysis of Swept-Cylinder Boundary Layers Computed By Navier-Stokes Code[R]. AIAA2001-2703, 2001.
[109]董亚妮,周恒.二维超音速边界层中三波共振和二次失稳机制的数值模拟研究[J].应用数学和力学, 2006, 27(2): 127-133.
[110]曹伟,黄章峰,周恒.超音速平板边界层转捩中层流突变为湍流的机理研究[J].应用数学和力学, 2006, 27(4): 379-386.
[111]罗纪生,陆昌根,周恒.流动稳定性中小扰动波传播速度的数值研究[J].空气动力学学报, 2002, 20(1): 1-8.
[112]曹伟,周恒.二维高超音速边界层扰动演化的数值研究及小激波的存在对流场结构的影响[J].中国科学G辑, 2004, 34(2): 203-212.
[113]黄章峰,曹伟,周恒.超音速平板边界层转捩中层流突变为湍流的机理——时间模式[J].中国科学G辑,2005,35(5):537-547.
[114]王新军,罗纪生,周恒.平面槽道流中层流-湍流转捩的“Breakdown”过程的内在机理[J].中国科学G辑, 2005, 35(1): 71-78.
[115]张永明,周恒.抛物化稳定性方程在可压缩边界层中应用的检验[J].应用数学和力学, 2007, 28(8): 883-893.
[116]李明军,高智.流体运动稳定性方程组椭圆特性的分析与应用[J].应用数学和力学, 2003, 24(11): 1179-1185.
[117]李明军,高智.二维抛物化稳定性方程的特征和次特征[J].应用力学学报, 2002, 19(3): 124-126.
[118]郭琳琳,唐登斌,王伟志.带压力梯度的非平行流边界层稳定性研究[J].南京航空航天大学学报, 2005, 37(2): 169-173.
[119]夏浩,唐登斌,陆昌根.三维扰动波的非平行边界层稳定性研究[J].力学学报, 2002, 34(5): 688-695.
[120]郭乃龙.三维不可压边界层抛物化稳定性方程的椭圆特性研究[J].航空学报, 1999, 20(2): 104-106.
[121]夏浩,唐登斌,陆昌根.边界层流动的非平行稳定性研究[J].空气动力学学报, 2001, 19(2): 186-190.
[122] Roe P L. Approximate Riemann Solvers, Parameter Vectors and Difference Schemes[J]. Journal of Computational Physics, 1981, 43(2): 357-372.
[123] Casper J, Shu C W, Atkins H. Comparison of Two Formulations for High-Order Accurate Essentially Nonoscillatory Schemes[J]. AIAA Journal, 1994, 32(10): 1970-1977.
[124] Shu C W, Zeng Y. High-Order Essentially Non-Oscillatory Scheme for Viscoelasticity with Fading Memory[J]. Quarterly of Applied Mathematics, 1997, 55(3): 459-484.
[125] Osher S. Riemann Solvers, the Entropy Condition and Difference Approximations[J]. SIAM Journal on Numerical Analysis, 1984, 21(2): 217-238.
[126] Tadmor E. Convenient Total Variation Diminishing Conditions for Nonlinear Difference Schemes[J]. SIAM Journal on Numerical Analysis, 1988, 25(5): 1002-1014.
[127] Lee D. Multidimensional Supercompact Wavelets for Fluid Dynamics[J]. Numerical Heat Transfer, Part B: Fundamentals, 2003, 43(4): 307-329.
[128] Shen M Y, Zhang Z B, Niu X L. A New Way for Constructing High Accuracy Shock-Capturing Generalized Compact Difference Schemes[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(25): 2703-2725.
[129] Shen M Y, Niu X L, Zhang Z B. Three-Point Fifth-Order Accurate Generalized Compact Scheme and Its Applications[J]. Acta Mechanica Sinica/Lixue Xuebao, 2001, 17(2): 142-150.
[130] Shu C W, Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hypersonic Conservation Laws[A]. In Advanced Numerical Approximation of Nonlinear Hypersonic Equations, Springer-Verlag, Berlin, 1998, 1697: 425.
[131] Chakravarthy S R, Euler Equations--Implicit Schemes and Boundary Conditions[J]. AIAA Journal 1983, 21(5): 699-706.
[132] Tompson K W. Time Dependent Boundary Conditions for Hyperbolic Systems[J]. Journal of Computational Physics, 1987, 68: 1-24.
[133] Poinsot T, Lele S K. Boundary Conditions for Direct Simulations of Compressible Viscous Flows[J]. Journal of Computational Physics, 1992, 101: 104-129.
[134]张涵信,沈孟育.计算流体力学——差分方法的原理和应用[M].近代空气动力学丛书,国防工业出版社,北京,2003.1
[135] Shu C-W, Osher S. Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes[J]. Journal of Computational Physics, 1988(2), 77: 439-471.
[136] Shu C-W, Osher S. Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes II[J], Journal of Computational Physics, 1989, 83: 32-78.
[137] Zhang H-X, Zhuang F-G. NND Schemes and Their Applications to Numerical Simulation of Two- and Three-Dimensional Flows[J]. Advances in Applied Mechanics, 1992, 29 (193): 764-785.
[138] Schulz-Rinne C W. Classification of the Riemann Problem for Two-Dimensional Gas Dynamics[J]. SIAM J. Math. Anal., 1993, 24: 76-88.
[139] Schulz-Rinne C W, Collins J P, and Glaz H M. Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics[J]. SIAM J. Sci. Comput., 1993, 14 (6): 1394-1414.
[140] Lax P D, Liu X D. Solution of Two-Dimensional Riemann Problems of Gas Dynamics by PositiveSchemes[J]. SIAM J. Sci. Comput. 1998, 19 (2): 319–340.
[141] Levy D, Puppo G, Russo G. A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Law[J]. SIAM J. Sci. Comput. 2002, 24 (2): 480-506.
[142] Woodward P, Collela P. The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks[J]. Journal of Computational Physics, 1984, 54:115-173.
[143] Langseth J O, Leveque R J. A Wave Propagation Method for Three-Dimensional Hyperbolic Conservation Laws[J]. Journal of Computational Physics, 2000, 165: 126-166.
[144] Edney B. Anomalous Heat Transfer and Pressure Distributions on Blunt Bodies at Hypersonic Speeds in the Presence of an Impinging Shock[R]. FFA Report 115, Aero. Res. Inst. of Sweden, 1968.
[145] Wieting A R, Holden M S. Experimental Shock-Wave Interference Heating on a Cylinder at Mach 6 and 8[J]. AIAA Journal, 1989, 27 (11): 1557-1565.
[146] Thareja R R, Stewart J R. A Point Implicit Unstructured Grid Solver for the Euler and Navier-Stokes Equations[J]. International Journal for Numerical Methods in Fluids, 1989 9(4): 405-425.
[147] Zhong X. Application of High-Order Accurate Essentially Nonoscillatory Schemes to Two-Dimensional Compressible Viscous Flows[R]. AIAA Paper, AIAA-93-0879, 1993.
[148] Gustafsson B. The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems[J]. Math. Comput. 1975, 29(130): 396-406.
[149] Stetson K F, Thompson E R, Donaldson J C, and Siler L G. Laminar Boundary Layer Stability Experiments on a Cone at Mach 8, Part 2: Blunt Cone[R]. AIAA Paper 84-0006, January 1984.
[150] Stetson K F, Kimmel R L. On Hypersonic Boundary Layer Stability[R]. AIAA Paper 92-0797, 1992.
[151] Wendt V, Kreplin H P, H?hler G, Grosche F R, et al. Planar and Conical Boundary Layer Stability Experiments at Mach 5[R]. AIAA Paper 93-5112,1993.
[152] Lachowicz J T, Chokani N, Wilkinson S P. Hypersonic Boundary Layer Stability Over a Flared Cone in a Quiet Tunnel[R]. AIAA 96-0782, 1996.
[153] Doggett P G, Chokani N. Hypersonic Boundary-Layer Stability Experiments on a Flared-Cone Model at Angle of Attack in a Quiet Wind Tunnel[R]. AIAA 97-0577, 1997.
[154] Wilkinson S P. A Review of Hypersonic Boundary Layer Stability Experiments in a Quiet Mach 6 Wind Tunnel[R]. AIAA Paper, AIAA 97-1819, 1997.
[155] Schneider S P. Design and Fabrication of a 9.5-Inch Mach-6 Quiet-Flow Ludwieg Tube[R]. AIAA 98-2511.
[156] Schneider S P. Development of a Mach-6 Quiet-Flow Wind Tunnel for Transition[A]. Research in Laminar-Turbulent Transition: Proceedings of the 1999 Iutam Conference, Sedona. Springer-Verlag, 2000.
[157] Schneider S P Fabrication and Testing of the Purdue Mach-6 Quiet-Flow Ludweig Tube[R]. AIAA 2000-0295.
[158] Schneider S P. Flight Data for Boundary-Layer Transition at Hypersonic and Supersonic Speeds[J]. Journal of Spacecraft and Rockets. 1999, 36(1): 8-20.
[159] Beckwith I E. Development of a High Reynolds Number Quiet Tunnel for Transition Research[J] AIAA Journal, 1975, 13(3): 300-306.
[160] Martellucci A, Maguire B L, and Neff R S. Analysis of Flight Test Transition and Turbulent Heating Data, Part I: Boundary Layer Transition Results[R]. NASA CR-129045 (NASA Database Citation 73N12287), Nov. 1972.
[161] Berkowitz A M, Kyriss C L, and Martellucci A. Boundary Layer Transition Flight Test Observations[R]. AIAA Paper 77-125, Jan. 1977.
[162] Batt R G, Legner H H. A Review of Roughness-Induced Nosetip Transition[J]. AIAA Journal, 1983, 21(1): 7–22.
[163] Williamsonw E. Hypersonic Flight Testing[R]. AIAA Paper 92-3989, June 1992.
[164] Iliff Kw, Shafer M F. A Comparison of Hypersonic Flight and Prediction Results. AIAA Paper 93-0311, Jan. 1993.
[165] Malik M R. Instability and Tansition in Supersonic Boundary Layers[J]. Laminar Turbulent Boundary Layers, Fluids Engineering Div., American Society of Mechanical Engineers, 1984, 11: 139-147.
[166] Malik M R. Prediction and Control of Transition in Supersonic and Hypersonic Boundary Layers[J]. AIAA Journal, 1989, 27(11): 1487–1493.
[167] Murphy J D, Rubesin Mw. An Evaluation of Free-Flight Test Data for Aerodynamic Heating From Laminar, Turbulent, and Transitional Boundary Layers. Part II—The X-17 Re-Entry Body[R].NASA CR-70931.
[168] Balgeman E J, Cassell G, Dension M R, et. al. X-17 Re-Entry Test Vehicle: R-2 Final Flight Report[R]. Technical Rept. MSD-3003, Lockheed Aircraft Corp. (NASA Database Citation 74N78004), April 1957. (NASA Database Citation 66n20084), April 1965.
[169] Murphy J D, Rubesin M W. Re-Evaluation of Heat-Transfer Data Obtained in Flight Tests of Heat-Sink Shielded Re-Entry Vehicles[J]. Journal of Spacecraft, 1966, 3(1): 53-60.
[170] Wright R L, Zoby E V. Flight Boundary Layer Transition Measurements on a Slender Cone at Mach 20[R]. AIAA Paper 77-719, June 1977.
[171] Sherman M M, Nakamura T. Flight Test Measurements of Boundary Layer Transition on a Non-Ablating 22-Deg. Cone[R]. AIAA Paper 68-1152, Dec. 1968.
[172] Sherman M M, Nakamura T. Flight Test Measurements of Boundary Layer Transition on a Nonablating 22-Deg. Cone[J] Journal of Spacecraft and Rockets, 1970, 7(2): 137-142.
[173] Haigh W W, Lake B M, and Ko D R S. Analysis of Flight Data on Boundary Layer Transition at High Angles of Attack[R]. NASA CR-1913, April 1972.
[174] Johnson C B, Darden C M. Flight Transition Data for Angles of Attack at Mach 22 with Correlations of the Data[R]. NASA TM-X-3235 (NASA Database Citation 75N28377), Aug. 1975.
[175] Bouslog S A, An M Y. Hartmann L N, et al. Review of Boundary Layer Transition Flight Data on the Space Shuttle Orbiter[R]. AIAA Paper 91-0741, 1991.
[176] Rabb L, Disher J H. Boundary-Layer Transition at High Reynolds Numbers As Obtained in Flight of a 20-Deg. Cone-Cylinder with Wall to Local Stream Temperature Ratios Near 1.0[R]. NACA RM-E55I15 (NASA Database Citation 93R18171), Nov. 1955.
[177] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 10-Deg Cone in Free Flight at Supersonic Mach Numbers up to 5.9[R]. NASA TN-D-745 (NASA Database Citation 62N71319), May 1961; Supersedes NACA RM-L56b07.
[178] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 10-Deg. Cone in Free Flight at Supersonic Mach Numbers up to 5.9[R]. NACA RML56B07 (NASA Database Citation 93R18462), April 1956.
[179] Rabb L, Krasnican M J. Observation of Laminar Flow on an Air-Launched 15-Deg. Cone Cylinder at Local Reynolds Numbers to 50 Million at Peak Mach Number of 6.75[R]. NACA RM-E56l03 (NASA Database Citation 62N64173), March 1957.
[180] Rabb L, Krasnican M J. Effects of Surface Roughness and Extreme Cooling on Boundary-Layer Transition for a 15-Deg. Cone–Cylinder in Free Flight at Mach Numbers to 7.6[R]. NACA RM-E57K19 (NASA Database Citation 62N64606), March 1958.
[181] Garland B J, Swanson a G, Speegle K C. Aerodynamic Heating and Boundary-Layer Transition on a 1/10-Power Nose Shape in Free Flight at Mach Numbers up to 6.7 and Freestream Reynolds Numbers up to 16 Million[R]. NASA TN-D-1378 (NASA Database citation 62N13291), June 1962; Supersedes NACA RM L57E14A, 1957.
[182] Disher J H, Rabb L. Observation of Laminar Flow on a Blunted 15-Deg. Cone–Cylinder in Free Flight at High Reynolds Number and Free-Stream Mach Numbers to 8.17[R]. NACA RM- E56G23 (NASA Database Citation 62N63995), Oct. 1956.
[183] Krasnican M J, Rabb L. Effects of Nose Radius and Extreme Cooling on Boundary-Layer Transition for Three Smooth 15-Deg.-Cone-Cylinders in Free Flight at Mach Numbers to 8.50[R]. NASA Memo-3-4-59e (NASA Database Citation 63N14756), March 1959.
[184] Bond A C, Rumsey C B. Free-Flight Skin Temperature and Pressure Measurements on a Slightly Blunted 25-Deg. Cone–Cylinder–Flare Configuration to a Mach Number of 9.89[R]. NACA RM-L57b18 (NASA Database Citation 93R18905), April 1957.
[185] Buglia J J. Heat Transfer and Boundary-Layer Transition on a Highly Polished Hemisphere-Cone in Free Flight at Mach Numbers up to 3.14 and Reynolds Numbers up to 24 Times 10-6[R]. NASA TN-D-955, Sept. 1961; Supersedes NACA RM L57D05.
[186] Garland B J, Chauvin L T. Measurements of Heat Transfer and Boundary-Layer Transition on an 8-Inch-Diameter Hemisphere-Cylinde R in Free Flight for a Mach Number Range of 2.00 to 3.88[R]. NACARM-L57D04A, March 1957.
[187] Hall J R, Speegle K C, and Piland R O. Preliminary Results From a Free-Flight Investigation of Boundary-Layer Transition and Heat Transfer on a Highly Polished 8-Inch-Diameter Hemisphere-Cylinder at Mach Numbers up to 3 and Reynolds Numbers Based on a Length of 1 Foot up to 17.7 Million[R]. NACA RM L57D18C (NASA Database Citation 93R19061), May 1957.
[188] Chauvin L T, Speegle K C. Boundary-Layer-Transition and Heat-Transfer Measurements From 179Flight Tests of Blunt and Sharp 50-Deg. Cones at Mach Numbers From 1.7 to 4.7[R]. NACA RM-L57D04 (NASA Database Citation 66N33310), April 1957.
[189] Sternberg J. A Free-Flight Investigation of the Possibility of High Reynolds Number Supersonic Laminar Boundary Layers[J]. Journal of the Aeronautical Sciences, 1952, 19(11): 721-733.
[190] Merlet C F, Rumsey C B. Supersonic Free-Flight Measurement of Heat Transfer and Transition on a 10-Deg Cone Having a Low Temperature Ratio[R]. NASA TN-D-951 (NASA Database Citation 62N71525), Aug. 1961; Supersedes NACA RM L56l10, 1956.
[191] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer on a 15-Deg Cone–Cylinder–Flare Configuration in Free Flight at Mach Numbers up to 4.7[R]. NASA TN-D-824 (NASA Database Citation 62N71398), May 1961; Supersedes NACA RM L57J10, 1958.
[192] Rabb L, Simpkinson S. Free-Flight Heat-Transfer Measurements on Two 20-Deg- Cone-Cylinders at Mach Numbers From 1.3 to 4.9[R]. NACA RM-E55F27 (NASA Database Citation 62N63397), July 1955.
[193] Rumsey C B, Lee D B. Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 15-Deg Cone in Free Flight at Supersonic Mach Numbers up to 5.2[R]. NASA TN-D-888 (NASA Database Citation 62N71462), Aug. 1961; Supersedes NACA RM L56F26, 1956.
[194] Braslow A L. Analysis of Boundary-Layer Transition on X-15-2 Research Airplane[R]. NASA TN-D-3487 (NASA Database Citation 66N30177), March 1966.
[195] Banner R D, Kuhl A E, and Quinn R D. Preliminary Results of Aerodynamic Heating Studies on the X-15 Airplane[R]. NASA TM-X-638, Jan. 1968.
[196] Gord P R. Measured and Calculated Structural Temperature Data From Two X-15 Airplane Flights with Extreme Aerodynamic Heating Conditions[R]. NASA TM-X-1358 (NASA Database Citation 74N71363), March 1967.
[197] Banner R D, Mctigue J G, and Petty G. Boundary-Layer-Transition Measurements in Full-Scale Flight[R]. NASA TM-79863 (NASA Database Citation 78N78570), Oct. 1978; Rev. NACA RM H58E28, July 1958.
[198] Fisher, D. F., and Dougherty, N. S.,“In-Flight Transition Measurement on a 10-Deg. Cone Atmach Numbers From0.5 to 2.0[R]. NASA TP-1971, 1982.
[199] Dougherty N S, Fisher D F. Boundary Layer Transition on a 10-Degree Cone: Wind Tunnel/ Flight Data Correlation[R]. AIAA Paper 80-0154, Jan. 1980.
[200] Quinn R D, Gong L. In-Flight Measurements on a Hollow Cylinder at a Mach Number of 3.0[R]. NASA TP-1764, Nov. 1980.
[201] Reed H, Saric W, Lyttle L, and Asada Y. Stability and Control of High-Speed Flows[R]. AIAA-2001-2700, 2001.
[202] Sugiura H,Tokugawa N, Ueda Y. Boundary-Layer Transition on an Axisymmetric Body at Incidence at Mach 1.2[J]. AIAA Journal 2006.5 44(5): 973-980.
[203] Ciolkosz L D, Spina E F. An Experimental Study of Gortler Vortices in Compressible Flow[A]. Collection of Technical Papers - AIAA/ASME/SAE/ASEE 42nd Joint Propulsion Conference, 2007, v3 p2036-2045.
[204] Zhong X, Ma Y. Receptivity and Linear Stability of Stetson's Mach 8 Blunt Cone Stability Experiments[R]. AIAA Paper, AIAA 2002-2849, 2002.
[205] Zhong X L, Tatineni M. Stable High-Order schemes and DNS of Boundary-Layer Stability on a Blunt Cone at Mach 8[R]. AIAA Paper, 2001-0437, 2001.
[206] Johnson H B, Seipp T G, and Candler G V. Numerical Study of Hypersonic Reacting Boundary Layer Transition on Cones[J]. Physics of Fluids, 1998 10(10): 2676-2685.
[207] Balakumar P. Stability of Supersonic Boundary Layers Over Blunt Wedges[A]. 36th AIAA Fluid Dynamics Conference Collection of Technical Papers - 36th AIAA Fluid Dynamics Conference,Jun, 2006, p487-496.
[208] Landau L D. On the problem of Turbulence. A kadem Iaa Nuuk SSSR. Dokaldy 1944, 44: 311-314.
[209] Stuart J T. On the Nonlinear Mechanics of Wave Disturbances in Stable and Unstable Parallel Flows, Part I: the Basic Behavior in Plane Poiseuille Flow[J]. Journal of Fluids Dynamics, 1960, (9): 353-370.
[210] Reshotko E. Boundary Layer Instability, Transition, and Control[R]. AIAA Paper 94-0001, Jan. 1994.
[211] Arnal D, Casalis G. Laminar-Turbulent Transition Prediction in Three-Dimensional Flows Progress in Aerospace Sciences, 2000, (36): 173-191.
[212] Reshotko E. Transition Issues at Hypersonic Speeds. Collection of Technical Papers[A]. 44th AIAA 180Aerospace Sciences Meeting, v12 p8472-8480, Jan, 2006.
[213] Reshotko E. Transition Issues for Atmospheric Entry[R]. 45th AIAA Aerospace Sciences Meeting and Exhibit, 8 - 11 January 2007, AIAA 2007-0304.
[214]傅德薰,马延文.平面混合流拟序结构的直接数值模拟.中国科学A辑,1996,26(7):659-664.
[215]曹伟.二维超音速混合层增强混合的研究[博士].天津大学,2001.
[216]赵耕夫.可压缩平板边界层的二次亚谐不稳定性[J].天津大学学报,2003, 36(3):276-280.
[217]苏彩虹,周恒.零攻角小钝头钝锥高超音速绕流边界层的稳定性分析和转捩预报[J].应用数学和力学, 2007, 28(5): 505-513.
[218]李新亮,,傅德薰,马延文.可压缩钝楔边界层转捩到湍流的直接数值模拟[J].中国科学G辑, 2004, 34(4): 466-480.
[219]刘嘉,雷麦芳,姚文秀,王发民.高超声速边界层流动转捩研究[J].计算物理, 2004, 21(1): 61-67.
[220]王发民,蔡春培,赵烈等.可压缩流动转捩的迭代求解[J].空气动力学学报, 1998, 16(4): 485-491.
[221]郭辉,连淇祥, Kachanov Y S, and Borodulin V I.边界层转捩过程三维扰动的发展和演化[J].北京航空航天大学学报, 2003, 29(6): 501-504.
[222] Ma Y, Fu D. Fourth Order Accurate Compact Scheme with Group Velocity Control (GVC)[J]. Science in China, Series A: Mathematics, Physics, Astronomy, 2001, 44(9): 1197-1204.
[223] Lynbimov A N, Ruasnov V V. Gas Flow Past Blunt Bodies[R]. NASA-TT-F715, 1973.
[224] Fay J A, Riddell R F. Theory of Stagnation Point Heat Transfer in Dissociated Air[J]. Journal of Aeronautical Sciences, 1958, 25: 73-85.
[225]张涵信,国义军.垂直于物面的横截面上流态的拓扑[J].空气动力学学报,2000, 18(1): 1-13.
[226] AIAA. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations[R]. AIAA G-007-1998 Reston, VA, 1998.
[227] Oberkampf W L, Trucano T G. Verification and Validation in Computational Fluid Dynamics[J]. Progress in Aerospace Sciences, 2002, 38: 209-272.
[228]侯中喜,夏刚,王承尧. CFD解的数值可靠性分析[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p790-795.
[229]邓小刚,宗文刚,张来平等.计算流体力学中的验证与确认[J].力学进展, 2007, 37(2): 279-288.
[230]于沛. CFD软件的算例验证确认技术[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p786-789.
[231]张涵信.航空航天工程中CFD的现状、面临的问题和发展[A].香山科学会议,第308次会议,航空航天工程应用中的湍流与CFD研究——现状、问题与发展对策.2007.9.
[232]恽起麟.风洞实验[M].近代空气动力学丛书.国防工业出版社.北京, 2000年9月.
[233]程厚梅等.风洞实验干扰与修正[M].近代空气动力学丛书.国防工业出版社.北京, 2003.1.
[234] Laflin K.R et al. Summary of Data From the Second AIAA CFD Dreg Prediction Workshop (Invited) [R]. AIAA 2004-0555.
[235] Tinoco E. N. Su T Y. Drag Prediction with the ZEUS/CFL3D System[R]. AIAA 2004-0552.
[236]张涵信,呙超,宗文刚.网格与高精度差分计算问题[J].力学学报,1999, 31(4): 398-405.
[237]张涵信,李沁.关于CFD数值解中网格、算法的协调问题[R].北京航空航天大学国际计算流体力学实验室交流报告,北京, 2007.
[238] AIAA. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations[R]. AIAA G-007-1998 Reston, VA, 1998.
[239] Oberkampf W L, Trucano T G. Verification and Validation in Computational Fluid Dynamics[J]. Progress in Aerospace Sciences, 2002, 38: 209-272.
[240]侯中喜,夏刚,王承尧. CFD解的数值可靠性分析[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p790-795.
[241]白文.气动计算软件可信度分析解决方案[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p770-774.
[242]于沛. CFD软件的算例验证确认技术[A].第十二届全国计算流体力学会议论文集,西安,2004.8, p786-789.
[243]张涵信.航空航天工程中CFD的现状、面临的问题和发展[A].香山科学会议,第308次会议,航空航天工程应用中的湍流与CFD研究——现状、问题与发展对策. 2007.9.
[244] Haj-Hariri H. Characteristics Analysis of the Parabolized Stability Equations[J]. Studies in Appl Math, 1994 , 92 (1) : 41-53.
[245] Li F, Malik M R. Spectral Analysis of Parabolized Stability Equations [J]. Computer & Fluids, 26(3): 279-297, 1997.
[246] Th. Herbert. On Finite Amplitudes in Boundary Layers[R]. ESA, TT-169, 1975.
[247] Pagella A, Rist U, and Wagner S. Numerical Investigations of Small-Amplitude Disturbances in a Laminar Boundary Layer with Impinging Shock Wave at Ma=4.8[J]. Physics of Fluid, 2002, 14(7): 2088-2101.
[248]袁湘江,周恒.考虑流向曲率和压力梯度的可压缩边界层稳定性分析[J].空气动力学学报,1998, 16(3): 276-281.
[249]张涵信.关于CFD验证确认中几个概念和计算结果的不确定度问题.空气动力学学报,(待发)
[250] Anderson J D. Hypersonic and high-temperature gas dynamics[M]. AIAA, 2006