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Academic literature on the topic 'Transonic small disturbance equation'

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Published: 4 June 2021
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Journal articles on the topic "Transonic small disturbance equation"

1

Balakrishnan, A. V. "Transonic Small Disturbance Potential Equation." AIAA Journal 42, no. 6 (June 2004): 1081–88. http://dx.doi.org/10.2514/1.5101.

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Lyrintzis, A. S., A. M. Wissink, and A. T. Chronopoulos. "Efficient iterative methods for the transonic small disturbance equation." AIAA Journal 30, no. 10 (October 1992): 2556–58. http://dx.doi.org/10.2514/3.11263.

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Čanić, Sunčica, Barbara Lee Keyfitz, and Eun Heui Kim. "Free boundary problems for the unsteady transonic small disturbance equation: Transonic regular reflection." Methods and Applications of Analysis 7, no. 2 (2000): 313–36. http://dx.doi.org/10.4310/maa.2000.v7.n2.a4.

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Chern, Mary, and Barbara Lee Keyfitz. "The unsteady transonic small disturbance equation: Data on oblique curves." Discrete and Continuous Dynamical Systems 36, no. 8 (March 2016): 4213–25. http://dx.doi.org/10.3934/dcds.2016.36.4213.

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Fishelov, Dalia. "Spectral Methods for the Small Disturbance Equation of Transonic Flows." SIAM Journal on Scientific and Statistical Computing 9, no. 2 (March 1988): 232–51. http://dx.doi.org/10.1137/0909015.

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Lyrintzis, A. S., and Y. Xue. "Acoustics of Transonic Flow Around an Oscillating Flap." Journal of Fluids Engineering 114, no. 2 (June 1, 1992): 240–45. http://dx.doi.org/10.1115/1.2910021.

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Investigation of noise mechanisms due to unsteady transonic flow is important for aircraft noise reduction. In this work, the near-field impulsive noise due to an oscillating flap is simulated numerically. The problem is modeled by the two-dimensional high frequency transonic small disturbance equation (VTRAN2 code). The three types of unsteady shock wave motion have been identified. Two different important disturbances exist in the pressure signal. The disturbances are related to the unsteady motion of the supersonic pocket and fluctuating lift, and drag forces. Pressure wave signatures, noise frequency spectra, and noise directivity are shown.
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Goorjian, Peter M., and Robert D. Van Buskirk. "Second-order-accurate spatial differencing for the transonic small-disturbance equation." AIAA Journal 23, no. 11 (November 1985): 1693–99. http://dx.doi.org/10.2514/3.9153.

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Batina, John T. "Efficient algorithm for solution of the unsteady transonic small-disturbance equation." Journal of Aircraft 25, no. 7 (July 1988): 598–605. http://dx.doi.org/10.2514/3.45629.

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Liu, Ya, Shijun Luo, and Feng Liu. "Multiple solutions and stability of the steady transonic small-disturbance equation." Theoretical and Applied Mechanics Letters 7, no. 5 (September 2017): 292–300. http://dx.doi.org/10.1016/j.taml.2017.09.011.

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Čanić, Sunčica, and Barbara Lee Keyfitz. "An Elliptic Problem Arising from the Unsteady Transonic Small Disturbance Equation." Journal of Differential Equations 125, no. 2 (March 1996): 548–74. http://dx.doi.org/10.1006/jdeq.1996.0040.

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Dissertations / Theses on the topic "Transonic small disturbance equation"

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Hanley, Patrick. "A multidomain pseudospectral solution for the general-frequency unsteady transonic small disturbance equation." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/39019.

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Ly, Eddie, and Eddie Ly@rmit edu au. "Numerical schemes for unsteady transonic flow calculation." RMIT University. Mathematics and Geospacial Sciences, 1999. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20081212.163408.

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An obvious reason for studying unsteady flows is the prediction of the effect of unsteady aerodynamic forces on a flight vehicle, since these effects tend to increase the likelihood of aeroelastic instabilities. This is a major concern in aerodynamic design of aircraft that operate in transonic regime, where the flows are characterised by the presence of adjacent regions of subsonic and supersonic flow, usually accompanied by weak shocks. It has been a common expectation that the numerical approach as an alternative to wind tunnel experiments would become more economical as computers became less expensive and more powerful. However even with all the expected future advances in computer technology, the cost of a numerical flutter analysis (computational aeroelasticity) for a transonic flight remains prohibitively high. Hence it is vitally important to develop an efficient, cheaper (in the sense of computational cost) and physically accurate flutter simulation tech nique which is capable of reproducing the data, which would otherwise be obtained from wind tunnel tests, at least to some acceptable engineering accuracy, and that it is essentially appropriate for industrial applications. This need motivated the present research work on exploring and developing efficient and physically accurate computational techniques for steady, unsteady and time-linearised calculations of transonic flows over an aircraft wing with moving shocks. This dissertation is subdivided into eight chapters, seven appendices and a bibliography listing all the reference materials used in the research work. The research work initially starts with a literature survey in unsteady transonic flow theory and calculations, in which emphasis is placed upon the developments in these areas in the last three decades. Chapter 3 presents the small disturbance theory for potential flows in the subsonic, transonic and supersonic regimes, including the required boundary conditions and shock jump conditions. The flow is assumed irrotational and inviscid, so that the equation of state, continuity equation and Bernoulli's equation formulated in Appendices A and B can be employed to formulate the governing fluid equation in terms of total velocity potential. Furthermore for transonic flow with free-stream Mach number close to unity, we show in Appendix C that the shocks that appear are weak enough to allow us to neglect the flow rotationality. The formulations are based on the main assumption that aerofoil slopes are everywhere small, and the flow quantities are small perturbations about their free-stream values. In Chapter 4, we developed an improved approximate factorisation algorithm that solves the two-dimensional steady subsonic small disturbance equation with nonreflecting far-field boundary conditions. The finite difference formulation for the improved algorithm is presented in Appendix D, with the description of the solver used for solving the system of difference equations described in Appendix E. The calculation of steady and unsteady nonlinear transonic flows over a realistic aerofoil are considered in Chapter 5. Numerical solution methods, based on the finite difference approach, for solving the two-dimensional steady and unsteady, general-frequency transonic small disturbance equations are presented, with the corresponding finite difference formulation described in Appendix F. The theories and solution methods for the time-linearised calculations, in the frequency and time domains, for the problem of unsteady transonic flow over a thin planar wing undergoing harmonic oscillation are presented in Chapters 6 and 7, respectively. The time-linearised calculations include the periodic shock motion via the shock jump correction procedure. This procedure corrects the solution values behind the shock, to accommodate the effect of shock motion, and consequently, the solution method will produce a more accurate time-linearised solution for supercritical flow. Appendix G presents the finite difference formulation of these time-linearised solution methods. The aim is to develop an efficient computational method for calculating oscillatory transonic aerodynamic quantities efficiently for use in flutter analyses of both two- and three-dimensional wings with lifting surfaces. Chapter 8 closes the dissertation with concluding remarks and future prospects on the current research work.
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Lee, Yun Sheng. "Correção de efeitos viscosos na solução do escoamento potencial de pequenas perturbações em regime transônico no domínio da freqüência." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/18/18135/tde-23072007-215517/.

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Um método de correção viscosa é aplicado na solução da equação potencial transônica de pequenas perturbações (TSD) no domínio da frequência. O objetivo é melhorar os resultados transônicos em que a interação choque/camada-limite é importante. A espessura de deslocamento da camada limite é estimada, a partir dos resultados da análise do escoamento invíscido, usando um método integral. A espessura de deslocamento é usada, então, para modificar a geometria das superfícies de sustentação e um novo resultado invíscido é obtido. Esse processo é repetido até que se atinja a convergência. No passado esse método foi aplicado, com bons resultados, na análise no domínio do tempo. No domínio da frequência os termos espaciais não lineares são preservados usando uma técnica de transformação conhecida como média harmônica. A principal razão para usar equação TSD ainda é o custo computacional, especialmente em se tratando de configurações completas de aeronaves. Um código de computador original é desenvolvido para análise bidimensional e um código de computador tridimensional existente é modificado para incluir a correção viscosa. A equação TSD é aproximada usando o método das diferenças finitas e resolvida usando sobre-relaxação sucessiva por linhas. Nos dois códigos é utilizada correção para vorticidade e variação de entropia. Os resultados têm boa correlação com dados experimentais publicados para a distribuição de pressão em regime transônico estacionário.
A viscous correction method is applied to the solution of the transonic small disturbance (TSD) potential equation in the frequency domain. The objective is to improve transonic results for which shock/boundary-layer interaction is important. Boundary-layer displacement thickness is calculated, with an integral method, using the results from an inviscid flow analysis. The calculated displacement thickness is then used to modify the lifting surface geometry and a new inviscid result is obtained. This process is repeated until convergence is achieved. In the past that method has been applied to time domain analysis with good results. In frequency domain the spatial nonlinear terms are preserved using a transformation technique known as harmonic averaging. The main reason for using the TSD equation still is computational cost, especially when dealing with complete aircraft configurations. An original computer code is developed for two-dimensional analysis and an existing three-dimensional computer code is extended to include the viscous correction. The transonic small disturbance potential equation is approximated using the finite difference method and solved through successive line over-relaxation. Both codes include correction for vorticity and variation in entropy. Results for several airfoil sections are obtained. The results compare well with published experimental data for steady transonic pressure distribution.
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Andreyev, Aleksandr Vladimirovich. "Theoretical And Computational Study of Steady Transonic Flows of Bethe-Zel\'dovich-Thompson Fluids." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/23734.

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We examine steady transonic flows of Bethe-Zel\'dovich-Thompson (BZT) fluids over thin turbine blades or airfoils. BZT fluids are ordinary fluids having a region of negative fundamental derivative over a finite range of pressures and temperatures in the single phase regime. We derive the transonic small disturbance equation (TSDE) capable of capturing the qualitative behavior of BZT fluids. The shock jump conditions, and shock existence conditions consistent with the derived TSDE are presented. The flux function is seen to be quartic in the pressure or density perturbation rather than the quadratic (convex) flux function of the perfect gas theory. We show how this nonconvex flux function can be used to predict and explain the complex flows possible in transonic BZT fluids. Numerical solutions using a successive line relaxation (SLR) scheme are presented. New results of interest include shock-splitting, collisions between expansion and compression shocks, the prediction and observation of two compressive bow shocks in supersonic flows, and the observation of as many as three normal stern shocks following an oblique trailing edge shock.
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Books on the topic "Transonic small disturbance equation"

1

Bland, Samuel R. Personal computer study of finite-difference methods for the transonic small disturbance equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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Bland, Samuel R. Personal computer study of finite-difference methods for the transonic small disturbance equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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Phillips, Pamela S. A transonic-small-disturbance wing design methodology. Hampton, Va: Langley Research Center, 1988.

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Center, Langley Research, ed. An efficient algorithm for solution of the unsteady transonic small-disturbance equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. A finite-difference approximate-factorization algorithm for solution of the unsteady transonic small-disturbance equation. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. A finite-difference approximate-factorization algorithm for solution of the unsteady transonic small-disturbance equation. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. A finite-difference approximate-factorization algorithm for solution of the unsteady transonic small-disturbance equation. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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T, Batina John, and Langley Research Center, eds. User's manual for XTRAN2L (Version 1.2): A program for solving the general-frequency unsteady transonic small-disturbance equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1986.

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G, Waggoner Edgar, Campbell Richard L. 1952-, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. A transonic-small-disturbance wing design methodology. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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G, Waggoner Edgar, Campbell Richard L. 1952-, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. A transonic-small-disturbance wing design methodology. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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Book chapters on the topic "Transonic small disturbance equation"

1

Čanić, Sunčica, Eun Heui Kim, and Barbara Lee Keyfitz. "Weak Shock Reflection Modeled by the Unsteady Transonic Small Disturbance Equation." In Hyperbolic Problems: Theory, Numerics, Applications, 217–26. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8370-2_23.

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Iatrou, Michail, Christian Breitsamter, and Boris Laschka. "Small Disturbance Navier-Stokes Equations: Application on Transonic Two-dimensional Flows Around Airfoils." In New Results in Numerical and Experimental Fluid Mechanics V, 471–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-33287-9_58.

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Garrett, Steven L. "Nonlinear Acoustics." In Understanding Acoustics, 701–53. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44787-8_15.

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Abstract A fundamental assumption of linear acoustics is that the presence of a wave does not have an influence on the properties of the medium through which it propagates. By extension, the assumption of linearity also means that a waveform is stable since any individual wave does not interact with itself. Small modifications in the sound speed due to wave-induced fluid convection (particle velocity) and to the wave’s effect on sound speed through the equation of state can lead to effects that could not be predicted within the limitations imposed by the assumption of linearity. Although a wave’s influence on the propagation speed may be small, those effects are cumulative and create distortion that can produce shocks. These are nonlinear effects because the magnitude of the nonlinearity’s influence is related to the square of an individual wave’s amplitude (self-interaction) or the product of the amplitudes of two interacting waves (intermodulation distortion). In addition, the time-average of an acoustically induced disturbance may not be zero. Sound waves can exert forces that are sufficient to levitate solid objects against gravity. The stability of such levitation forces will also be examined along with their relation to resonance frequency shifts created by the position of the levitated object.
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Canic, Suncica, Barbara Lee Keyfitz, and Katarina Jegdic. "Transonic regular reflection for the unsteady transonic small disturbance equation‚Äîdetails of the subsonic solution." In Lecture Notes in Pure and Applied Mathematics, 125–63. Chapman and Hall/CRC, 2007. http://dx.doi.org/10.1201/9781420011159.ch6.

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"Transonic regular reflection for the unsteady transonic small disturbance equation—details of the subsonic solution Katarina Jegdic´, Barbara Lee Keyfitz, and Sunc˘ica C˘anic´." In Free and Moving Boundaries, 143–82. Chapman and Hall/CRC, 2007. http://dx.doi.org/10.1201/9781420011159-10.

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Luo, Shijun, Huili Shen, and Ping Liu. "Transonic Small Transverse Perturbation Equation and its Computation." In Frontiers of Computational Fluid Dynamics 1998, 125–39. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789812815774_0007.

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Conference papers on the topic "Transonic small disturbance equation"

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Ghayour, Kaveh, and Oktay Baysal. "Unsteady aerodynamics and shape optimization using modified transonic small disturbance equation." In 37th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-654.

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Wissink, A., Anastasios Lyrintzis, and A. Chronopoulos. "High performance computing techniques for solving the Transonic Small Disturbance equation." In 33rd Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1995. http://dx.doi.org/10.2514/6.1995-576.

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BATINA, JOHN. "An efficient algorithm for solution of the unsteady transonic small-disturbance equation." In 25th AIAA Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1987. http://dx.doi.org/10.2514/6.1987-109.

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Fujiwara, Gustavo E., Daniel Chaparro, and Nhan T. Nguyen. "An Integral Boundary Layer Direct Method Applied to 2D Transonic Small-Disturbance Equations." In 34th AIAA Applied Aerodynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-3568.

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Hall, Kenneth C., William S. Clark, and Christopher B. Lorence. "A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-094.

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A computational method for efficiently predicting unsteady transonic flows in two- and three-dimensional cascades is presented. The unsteady flow is modelled using a linearized Euler analysis whereby the unsteady flow field is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The equations that govern the perturbation flow, the linearized Euler equations, are linear variable coefficient equations. For transonic flows containing shocks, shock capturing is used to model the shock impulse (the unsteady load due to the harmonic motion of the shock). A conservative Lax-Wendroff scheme is used to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse are investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essential role of unsteady shock impulse loads on the flutter stability of fans.
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Zhu, N. G., L. Xu, and M. Z. Chen. "Similarity Transformations for Compressor Blading." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-123.

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Improving the performance of high speed axial compressors through low speed model compressor testing has proved to be economical and effective (Wisler, 1984). The key to this technique is to design low speed blade profiles which are aerodynamically similar to their high speed counterparts. The conventional aerodynamic similarity transformation involves the small disturbance potential flow assumption therefore its application is severely limited and generally not used in practical design. In this paper, a set of higher order transformation rules are presented which can accommodate large disturbances at transonic speed and are therefore applicable to similar transformations between the high speed HP compressor and its low speed model. Local linearization is used in the non–linear equations and the transformation is obtained in an iterative process. The transformation gives the global blading parameters such as camber, incidence and solidity as well as the blade profile. Both numerical and experimental validations of the transformation show that the non–linear similarity transformations do retain satisfactory accuracy for highly loaded blades up to low transonic speeds. Further improvement can be made by only slightly modifing profiles numerically without altering the global similarity parameters.
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FUGLSANG, D., and M. WILLIAMS. "Non-isentropic unsteady transonic small disturbance theory." In 26th Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1985. http://dx.doi.org/10.2514/6.1985-600.

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Rusak, Zvi, and J. C. Lee. "A Small-Disturbance Model of Transonic Combustion." In 34th AIAA Fluid Dynamics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-2336.

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Luo, Shijun, Lixia Wang, Shijun Luo, and Lixia Wang. "Shock wave in transonic small-disturbance flow." In 15th Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-2242.

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Evers, I. "Gust-shock interaction in transonic small-disturbance flow." In 5th AIAA/CEAS Aeroacoustics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-1972.

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Reports on the topic "Transonic small disturbance equation"

1

Suncica Canic and B. L. Keyfitz. An elliptic problem arising from the unsteady transonic small disturbance equation. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/764166.

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