Relevant bibliographies by topics / Sonic Boom Problem

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Conference papers

Academic literature on the topic 'Sonic Boom Problem'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Sonic Boom Problem"

1

Потапкин, А. В., and Д. Ю. Москвичев. "Звуковой удар от тонкого тела и локальных областей нагрева сверхзвукового набегающего потока." Журнал технической физики 91, no. 4 (2021): 558. http://dx.doi.org/10.21883/jtf.2021.04.50618.248-20.

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The problem of a sonic boom generated by a slender body and local regions of supersonic flow heating is solved numerically. The free-stream Mach number of the air flow is 2. The calculations are performed by a combined method of phantom bodies. The results show that local heating of the incoming flow can ensure sonic boom mitigation. The sonic boom level depends on the number of local regions of incoming flow heating. One region of flow heating can reduce the sonic boom by 20% as compared to the sonic boom level in the cold flow. Moreover, consecutive heating of the incoming flow in two regions provides sonic boom reduction by more than 30%.
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2

Anderson, Mark, Kent Gee, Jeffrey Durrant, and Alexandra Loubeau. "Towards high-quality X-59 sonic thump measurements." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 266, no. 1 (May 25, 2023): 1145–49. http://dx.doi.org/10.3397/nc_2023_0144.

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Brigham Young University has been studying questions related to NASA X-59 community noise testing. A summary of the key findings and recommendations to date are presented. Among these are weather-resistant ground microphone setups that reduce wind noise, methods for treating the problem of ambient noise contamination on sonic boom metrics and spectra, and the turbulence-induced variability seen over relatively small-aperture arrays. Also discussed are recommendations for data post-processing, e.g., employing a digital pole-shifting filter and zero-padding to improve the fidelity and smoothness of low-frequency spectral data. Finally, the relative merits of various sonic boom metrics are considered. Although Perceived Level has been the most widely-used metric, it is relatively sensitive to ambient noise contamination and turbulence-induced variability. [Work supported by NASA Langley Research Center through the National Institute of Aerospace.]
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3

Anderson, Mark C., Kent L. Gee, J. T. Durrant, and Alexandra Loubeau. "Overview of research-based community noise testing recommendations from Brigham Young University." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A127. http://dx.doi.org/10.1121/10.0015771.

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Brigham Young University has been studying questions related to NASA X-59 community noise testing. A summary of the key findings and recommendations to date are presented. Among these are weather-resistant ground microphone setups that reduce wind noise, methods for treating the problem of ambient noise contamination on sonic boom metrics and spectra, and the turbulence-induced variability seen over relatively small-aperture arrays. Also discussed are recommendations for data post-processing, e.g., employing a digital pole-shifting filter and zero-padding to improve the fidelity and smoothness of low-frequency spectral data. Finally, the relative merits of various sonic boom metrics are considered. Although Perceived Level has been the most widely-used metric, it is relatively sensitive to ambient noise contamination and turbulence-induced variability. [Work supported by NASA Langley Research Center through the National Institute of Aerospace.]
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4

GIDDINGS, THOMAS E., ZVI RUSAK, and JACOB FISH. "A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases." Journal of Fluid Mechanics 429 (February 25, 2001): 255–80. http://dx.doi.org/10.1017/s0022112000002779.

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The interaction of weak shock waves with small heterogeneities in gaseous media is studied. It is first shown that various linear theories proposed for this problem lead to pathological breakdowns or singularities in the solution near the wavefront and necessarily fail to describe this interaction. Then, a nonlinear small-disturbance model is developed. The nonlinear theory is uniformly valid and accounts for the competition between the near-sonic speed of the wavefront and the small variations of vorticity and sound speed in the heterogeneous media. This model is an extension of the transonic small-disturbance problem, with additional terms accounting for slight variations in the media. The model is used to analyse the propagation of the sonic-boom shock wave through the turbulent atmospheric boundary layer. It is found that, in this instance, the nonlinear model accounts for the observed behaviour. Various deterministic examples of interaction phenomena demonstrate good agreement with available experimental data and explain the main observed phenomena in Crow (1969).
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5

Baskar, S., and Phoolan Prasad. "Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems." Proceedings of the Indian Academy of Sciences - Section A 116, no. 1 (February 2006): 97–119. http://dx.doi.org/10.1007/bf02829742.

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6

Li, Zhanke, Yang Liu, Yulin Ding, Zhijin Lei, and Boping Ma. "Influence of Quiet Spike on Supersonic Transport for Low Boom Effect." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 1 (February 2019): 203–10. http://dx.doi.org/10.1051/jnwpu/20193710203.

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One of the biggest technical challenges of supersonic flight is the mitigation of sonic boom. To deal with this problem, the Gulfstream Aerospace Corporation came up with the spike concept, and it showed to be efficient. However, there also remain several problems, the first one is that installing the spike makes it harder to balance for supersonic transport and the another one is that the movement equipment is complex. In this paper, a new concept by replacing the multi-stage of the normal spike with smooth transistion cones is proposed. The concept simultaneously uses the CFD solver HUNS3D based on the Reynolds average (RANS) equation and the far-field FL-BOOM sound explosion propagation program based on Thomas waveform parameter method. The effectiveness of the present scheme to suppress supersonic aircraft sound explosion is verified according to the concept. It is proved that the increased length is good for low blast and the main factor affecting the blast reduction effect of multistage mute cone is length rather than series by the analysis. The results have important reference value for the silent cone design of supersonic aircraft.
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7

Kadalbajoo, Mohan K., and Ashish Awasthi. "Parameter free hybrid numerical method for solving modified Burgers’ equations on a nonuniform mesh." Asian-European Journal of Mathematics 10, no. 02 (July 21, 2016): 1750029. http://dx.doi.org/10.1142/s1793557117500292.

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In this paper, the modified Burgers’ equation is considered. These kinds of problems come from the field of sonic boom and explosions theories. At big Reynolds’ number there is a boundary layer in the right side of the domain. From numerical point of view, the major difficulty in dealing with this type of problem is that the smooth initial data can give rise to solution varying regions i.e. boundary layer regions. To tackle this situation, we propose a numerical method on nonuniform mesh of Shishkin type, which works well at high as well as low Reynolds number. The proposed method comprises of Euler implicit scheme and hybrid scheme in time and space direction, respectively. First, we discretize the continuous problem in temporal direction by Euler implicit method, which yields a set of ode’s at each time level. The resulting set of differential equations are approximated by a hybrid scheme on Shishkin mesh i.e. upwind in regular region (nonboundary layer region) and central difference in boundary layer regions. The convergence of proposed method has been shown parameter uniform. Some numerical experiments have been carried out to corroborate the theoretical results.
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8

Chapman, C. J. "Shocks and singularities in the pressure field of a supersonically rotating propeller." Journal of Fluid Mechanics 192 (July 1988): 1–16. http://dx.doi.org/10.1017/s0022112088001752.

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When linear acoustic theory is applied to the thickness noise problem of a supersonic propeller, it can give rise to a surface on which the pressure is discontinuous or singular. A method is described for obtaining the equation of this surface (when it exists), and the pressure field nearby; jumps, logarithms and inverse square roots occur, and their coefficients may be calculated exactly. The special case of a blade with a straight radial edge gives a cusped cone, whose sheets, each with a different type of discontinuity or singularity in pressure, are separated by lines of cusps; the coefficients in formulae for the pressure near the surface tend to infinity as a cusp line is approached, in proportion to the inverse quarter power of distance from the line. These results determine regions of space where nonlinear effects are important, and they suggest a strong analogy with sonic boom.
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9

Drobzheva, Ya V., D. V. Zikunkova, and V. M. Krasnov. "TNT equivalent of the shock wave energy generated during the supersonic flight of an aircraft." Journal of Physics: Conference Series 2124, no. 1 (November 1, 2021): 012001. http://dx.doi.org/10.1088/1742-6596/2124/1/012001.

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Abstract To assess the impact on human health of the sonic boom that occurs when an aircraft is flying at supersonic speed, and, accordingly, to solve the problem of noise reduction by optimizing the aircraft design, it is proposed to evaluate the shock wave energy using the TNT equivalent of a cylindrical explosion. An example of calculating the shock wave energy during flights of F4 and F18 aircraft at different altitudes is considered. To calculate the evolution of an acoustic pulse during its propagation from the boundary of the shock wave transition to the acoustic one, the wave equation and its solution are used, taking into account the inhomogenei-ty of the atmosphere, nonlinear effects, absorption and expansion of the wave front, as well as the results of ground-based measurements of acoustic pulses. The results of calculations of the dependence of the explosion energy on the flight altitude, as well as on the type of aircraft are explained on the basis of the formula for the atmospheric resistance force.
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10

Fomin, V. M., V. F. Volkov, T. A. Kiseleva, and V. F. Chirkashenko. "Investigations of the Sonic Boom Problem at the Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences." Journal of Engineering Physics and Thermophysics 91, no. 4 (July 2018): 1110–20. http://dx.doi.org/10.1007/s10891-018-1838-4.

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Dissertations / Theses on the topic "Sonic Boom Problem"

1

Gupta, Hari Shanker. "Numerical Study Of Regularization Methods For Elliptic Cauchy Problems." Thesis, 2010. https://etd.iisc.ac.in/handle/2005/1249.

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Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic Cauchy problems are typically ill-posed, i.e., there may not be a solution for some Cauchy data, and even if a solution exists uniquely, it may not depend continuously on the Cauchy data. The ill-posedness causes numerical instability and makes the classical numerical methods inappropriate to solve such problems. For Cauchy problems, the research on uniqueness, stability, and efficient numerical methods are of significant interest to mathematicians. The main focus of this thesis is to develop numerical techniques for elliptic Cauchy problems. Elliptic Cauchy problems can be approached as data completion problems, i.e., from over-specified Cauchy data on an accessible part of the boundary, one can try to recover missing data on the inaccessible part of the boundary. Then, the Cauchy problems can be solved by finding a so-lution to a well-posed boundary value problem for which the recovered data constitute a boundary condition on the inaccessible part of the boundary. In this thesis, we use natural linearization approach to transform the linear Cauchy problem into a problem of solving a linear operator equation. We consider this operator in a weaker image space H−1, which differs from the previous works where the image space of the operator is usually considered as L2 . The lower smoothness of the image space will make a problem a bit more ill-posed. But under such settings, we can prove the compactness of the considered operator. At the same time, it allows a relaxation of the assumption concerning noise. The numerical methods that can cope with these ill-posed operator equations are the so called regularization methods. One prominent example of such regularization methods is Tikhonov regularization which is frequently used in practice. Tikhonov regularization can be considered as a least-squares tracking of data with a regularization term. In this thesis we discuss a possibility to improve the reconstruction accuracy of the Tikhonov regularization method by using an iterative modification of Tikhonov regularization. With this iterated Tikhonov regularization the effect of the penalty term fades away as iterations go on. In the application of iterated Tikhonov regularization, we find that for severely ill-posed problems such as elliptic Cauchy problems, discretization has such a powerful influence on the accuracy of the regularized solution that only with some reasonable discretization level, desirable accuracy can be achieved. Thus, regularization by projection method which is commonly known as self-regularization is also considered in this thesis. With this method, the regularization is achieved only by discretization along with an appropriate choice of discretization level. For all regularization methods, the choice of an appropriate regularization parameter is a crucial issue. For this purpose, we propose the balancing principle which is a recently introduced powerful technique for the choice of the regularization parameter. While applying this principle, a balance between the components related to the convergence rate and stability in the accuracy estimates has to be made. The main advantage of the balancing principle is that it can work in an adaptive way to obtain an appropriate value of the regularization parameter, and it does not use any quantitative knowledge of convergence rate or stability. The accuracy provided by this adaptive strategy is worse only by a constant factor than one could achieve in the case of known stability and convergence rates. We apply the balancing principle in both iterated Tikhonov regularization and self-regularization methods to choose the proper regularization parameters. In the thesis, we also investigate numerical techniques based on iterative Tikhonov regular-ization for nonlinear elliptic Cauchy problems. We consider two types of problems. In the first kind, the nonlinear problem can be transformed to a linear problem while in the second kind, linearization of the nonlinear problem is not possible, and for this we propose a special iterative method which differs from methods such as Landweber iteration and Newton-type method which are usually based on the calculation of the Frech´et derivative or adjoint of the equation. Abundant examples are presented in the thesis, which illustrate the performance of the pro-posed regularization methods as well as the balancing principle. At the same time, these examples can be viewed as a support for the theoretical results achieved in this thesis. In the end of this thesis, we describe the sonic boom problem, where we first encountered the ill-posed nonlinear Cauchy problem. This is a very difficult problem and hence we took this problem to provide a motivation for the model problems. These model problems are discussed one by one in the thesis in the increasing order of difficulty, ending with the nonlinear problems in Chapter 5. The main results of the dissertation are communicated in the article [35].
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2

Gupta, Hari Shanker. "Numerical Study Of Regularization Methods For Elliptic Cauchy Problems." Thesis, 2010. http://etd.iisc.ernet.in/handle/2005/1249.

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Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic Cauchy problems are typically ill-posed, i.e., there may not be a solution for some Cauchy data, and even if a solution exists uniquely, it may not depend continuously on the Cauchy data. The ill-posedness causes numerical instability and makes the classical numerical methods inappropriate to solve such problems. For Cauchy problems, the research on uniqueness, stability, and efficient numerical methods are of significant interest to mathematicians. The main focus of this thesis is to develop numerical techniques for elliptic Cauchy problems. Elliptic Cauchy problems can be approached as data completion problems, i.e., from over-specified Cauchy data on an accessible part of the boundary, one can try to recover missing data on the inaccessible part of the boundary. Then, the Cauchy problems can be solved by finding a so-lution to a well-posed boundary value problem for which the recovered data constitute a boundary condition on the inaccessible part of the boundary. In this thesis, we use natural linearization approach to transform the linear Cauchy problem into a problem of solving a linear operator equation. We consider this operator in a weaker image space H−1, which differs from the previous works where the image space of the operator is usually considered as L2 . The lower smoothness of the image space will make a problem a bit more ill-posed. But under such settings, we can prove the compactness of the considered operator. At the same time, it allows a relaxation of the assumption concerning noise. The numerical methods that can cope with these ill-posed operator equations are the so called regularization methods. One prominent example of such regularization methods is Tikhonov regularization which is frequently used in practice. Tikhonov regularization can be considered as a least-squares tracking of data with a regularization term. In this thesis we discuss a possibility to improve the reconstruction accuracy of the Tikhonov regularization method by using an iterative modification of Tikhonov regularization. With this iterated Tikhonov regularization the effect of the penalty term fades away as iterations go on. In the application of iterated Tikhonov regularization, we find that for severely ill-posed problems such as elliptic Cauchy problems, discretization has such a powerful influence on the accuracy of the regularized solution that only with some reasonable discretization level, desirable accuracy can be achieved. Thus, regularization by projection method which is commonly known as self-regularization is also considered in this thesis. With this method, the regularization is achieved only by discretization along with an appropriate choice of discretization level. For all regularization methods, the choice of an appropriate regularization parameter is a crucial issue. For this purpose, we propose the balancing principle which is a recently introduced powerful technique for the choice of the regularization parameter. While applying this principle, a balance between the components related to the convergence rate and stability in the accuracy estimates has to be made. The main advantage of the balancing principle is that it can work in an adaptive way to obtain an appropriate value of the regularization parameter, and it does not use any quantitative knowledge of convergence rate or stability. The accuracy provided by this adaptive strategy is worse only by a constant factor than one could achieve in the case of known stability and convergence rates. We apply the balancing principle in both iterated Tikhonov regularization and self-regularization methods to choose the proper regularization parameters. In the thesis, we also investigate numerical techniques based on iterative Tikhonov regular-ization for nonlinear elliptic Cauchy problems. We consider two types of problems. In the first kind, the nonlinear problem can be transformed to a linear problem while in the second kind, linearization of the nonlinear problem is not possible, and for this we propose a special iterative method which differs from methods such as Landweber iteration and Newton-type method which are usually based on the calculation of the Frech´et derivative or adjoint of the equation. Abundant examples are presented in the thesis, which illustrate the performance of the pro-posed regularization methods as well as the balancing principle. At the same time, these examples can be viewed as a support for the theoretical results achieved in this thesis. In the end of this thesis, we describe the sonic boom problem, where we first encountered the ill-posed nonlinear Cauchy problem. This is a very difficult problem and hence we took this problem to provide a motivation for the model problems. These model problems are discussed one by one in the thesis in the increasing order of difficulty, ending with the nonlinear problems in Chapter 5. The main results of the dissertation are communicated in the article [35].
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Books on the topic "Sonic Boom Problem"

1

Schmelz, Peter J. Sonic Overload. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197541258.001.0001.

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Sonic Overload presents a musically centered cultural history of the late Soviet Union. It focuses on polystylism in music as a response to the information overload swamping listeners in the Soviet Union during its final decades. The central themes are collage, popular music, kitsch, and eschatology. The book traces the ways in which leading composers Alfred Schnittke and Valentin Silvestrov initially embraced and assimilated popular sources before ultimately rejecting them. Polystylism first responded to the utopian impulses of Soviet doctrine with utopian impulses to encompass all musical styles, from “high” to “low.” But these initial all-embracing aspirations were soon followed by retreats to alternate utopias founded on carefully selecting satisfactory borrowings, as familiar hierarchies of culture, taste, and class reasserted themselves. Looking at polystylism in the late USSR tells us about past and present, near and far, as it probes the musical roots of the overloaded, distracted present. Sonic Overload is intended for musicologists and Soviet, Russian, and Ukrainian specialists in history, the arts, film, and literature, but it also targets a wider scholarly audience, including readers interested in twentieth- and twenty-first century music; modernism and postmodernism; quotation and collage; the intersections of “high” and “low” cultures; and politics and the arts. Based on archival research, oral historical interviews, and other overlooked primary materials, as well as close listening and thorough examination of scores and recordings, Sonic Overload presents a multilayered and comprehensive portrait of late-Soviet polystylism and cultural life, and of the music of Silvestrov and Schnittke.
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2

Kromhout, Melle Jan. The Logic of Filtering. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780190070137.001.0001.

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This book traces the profound impact of technical media on the sound of music, asking: How do media technologies shape sound? How does this affect music? And how did it change what we listen for in music? Based on the information theoretical proposition that all transmission channels introduce noise and distortion, the argument accounts for the fact that technologically reproduced music is inherently shaped by the technologies that enable its reproduction. The media archaeological assessment of this noise of sound media developed in the book draws from a wide range of sources, both theoretical and historical, conceptual and technical. Together, they show that noise should not be understood as unwanted by-effect but instead plays a foundational role in shaping the sonic contours of technologically reproduced music. Over the course of five chapters, the book sketches a broad history of the problem of noise in sound recording, looks at specific analog and digital noise-related technologies, traces the ideal of sonic purity back to key developments in nineteenth-century acoustics, and develops an analysis of the close interrelation between noise and the temporality of sound. This relation, it argues, is central to the way in which recorded sound and music resonate with listeners. Ultimately, this media-specific analysis of the noise of sound media thereby greatly enriches our understanding of the way in which they changed and continue to change the sonorous qualities of music, thus offering a new perspective on the interaction between music, media, and listeners.
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3

Sonic Mario Pokemon Activity Book: Leave All Your Stress Behind with Fun Activity Book for Learning, Coloring, Playing, Stimulating Problem-Solving Skills, and Having Fun with All Your Favorite Characters. Independently Published, 2020.

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4

Government, U. S., National Ae Space Administration (Nasa), and World Spaceflight News (Wsn). Supersonic Cruise Technology (NASA SP-472) - History of Breaking the Sound Barrier, U. S. and Foreign SST Transport Programs, B-70, TU-144, Concorde, Problems with Sonic Boom, Pollution, Aerodynamics. Independently Published, 2019.

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5

Hall, Roger. Soil Essentials. CSIRO Publishing, 2008. http://dx.doi.org/10.1071/9780643095632.

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Soil Essentials is a practical reference for farmers and land managers covering soil issues commonly encountered at the farm level. Written in a straightforward style, it explains the principles of soil management and the interpretation of soil tests, and how to use this information to address long-term soil and enterprise viability. This book demonstrates how minerals, trace elements, organic matter, soil organisms and fertilisers affect soil, plant and animal health. It shows how to recognise soil decline, and how to repair soils affected by nutrient imbalances, depleted soil microbiology, soil erosion, compaction, structural decline, soil sodicity and salinity. The major problem-soils – sodic soils, light sandy soils, heavy clay soils and acid sulphate soils – are all examined. With this information, farmers and land managers will be able to consider the costs and financial benefits of good soil management.
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Conference papers on the topic "Sonic Boom Problem"

1

Cheng, Hsien. "Sonic-Boom Generated Underwater Noise as Problem in Unsteady Aerodynamics." In 4th AIAA Theoretical Fluid Mechanics Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-4804.

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Bazhlekova, E., and I. Bazhlekov. "On the Rayleigh-Stokes problem for generalized fractional Oldroyd-B fluids." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934312.

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Kostova, S., L. Imsland, and I. Ivanov. "LQR problem of linear discrete time systems with nonnegative state constraints." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934346.

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Tikhovskaya, S. V., and A. I. Zadorin. "A two-grid method with Richardson extrapolation for a semilinear convection-diffusion problem." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934332.

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Efremov, A., E. Karepova, and A. Vyatkin. "Some features of the CUDA implementation of the semi-Lagrangian method for the advection problem." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934328.

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Vyatkin, A. "A semi-Lagrangian algorithm based on the integral transformation for the three-dimensional advection problem." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934337.

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7

Cheng, H., and C. Lee. "Problems in sonic boom theory studied as issues of singular perturbation." In Theroretical Fluid Mechanics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-2165.

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Ozcer, Isik, and Osama Kandil. "Fun3D / OptiGRID Coupling for Unstructured Grid Adaptation for Sonic Boom Problems." In 46th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-61.

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9

Mishchenko, P. A., and T. A. Gimon. "Development of sonic boom prediction code based on augmented Burgers equation: Molecular relaxation." In ACTUAL PROBLEMS OF CONTINUUM MECHANICS: EXPERIMENT, THEORY, AND APPLICATIONS. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0132924.

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Lyashenko, V., and O. Kobilskaya. "Contact of boundary-value problems and nonlocal problems in mathematical models of heat transfer." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934320.

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