Relevant bibliographies by topics / Rankine-Hugoniot

Academic literature on the topic 'Rankine-Hugoniot'

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Published: 6 September 2023

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Journal articles on the topic "Rankine-Hugoniot"

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Avramenko, Andriy A., Andrii I. Tyrinov, and Igor V. Shevchuk. "Analytical simulation of normal shock waves in turbulent flow." Physics of Fluids 34, no. 5 (May 2022): 056101. http://dx.doi.org/10.1063/5.0093205.

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The focus of the work is on analytical modeling of normal shock wave propagation in a turbulent adiabatic gas flow. For this, a modified Rankine–Hugoniot model was developed. A solution is obtained for the Rankine–Hugoniot conditions in a turbulent gas flow with different turbulence intensity. Variation of the velocity of an adiabatic turbulent gas flow during its passage through a normal shock wave is elucidated depending on the turbulence intensity. The equation of the modified Hugoniot adiabat is also obtained.
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Mellmann, Marcel, and Markus Scholle. "Symmetries and Related Physical Balances for Discontinuous Flow Phenomena within the Framework of Lagrange Formalism." Symmetry 13, no. 9 (September 9, 2021): 1662. http://dx.doi.org/10.3390/sym13091662.

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By rigorous analysis, it is proven that from discontinuous Lagrangians, which are invariant with respect to the Galilean group, Rankine–Hugoniot conditions for propagating discontinuities can be derived via a straight forward procedure that can be considered an extension of Noether’s theorem. The use of this general procedure is demonstrated in particular for a Lagrangian for viscous flow, reproducing the well known Rankine–Hugoniot conditions for shock waves.
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Gedalin, Michael, Nikolai V. Pogorelov, and Vadim Roytershteyn. "Rankine–Hugoniot Relations Including Pickup Ions." Astrophysical Journal 889, no. 2 (January 30, 2020): 116. http://dx.doi.org/10.3847/1538-4357/ab6660.

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Kentzer, Czeslaw P. "Quasilinear form of Rankine-Hugoniot jump conditions." AIAA Journal 24, no. 4 (April 1986): 691–93. http://dx.doi.org/10.2514/3.9332.

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Gao, Yang, and Chung K. Law. "RANKINE-HUGONIOT RELATIONS IN RELATIVISTIC COMBUSTION WAVES." Astrophysical Journal 760, no. 2 (November 15, 2012): 122. http://dx.doi.org/10.1088/0004-637x/760/2/122.

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SATOH, Akira. "Rankine-Hugoniot Relations for Lennard-Jones Liquids." Transactions of the Japan Society of Mechanical Engineers Series B 58, no. 549 (1992): 1419–25. http://dx.doi.org/10.1299/kikaib.58.1419.

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Satoh, Akira. "Rankine-Hugoniot Relations for Lennard-Jones Liquids." Journal of Fluids Engineering 116, no. 3 (September 1, 1994): 625–30. http://dx.doi.org/10.1115/1.2910323.

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The purpose of the present study is to clarify the Rankine-Hugoniot relations for Lennard-Jones liquids. First, Monte Carlo simulations are conducted to evaluate the state quantities such as the pressures, the internal energies, and the sound velocities. These computed values are used to obtain the approximate expressions for the state quantities by the method of least squares. The Rankine-Hugoniot relations are then clarified numerically as a function of the shock Mach number by solving the basic equations together with those approximate expressions. For liquid shock waves, not only the pressure but also the temperature increases much larger than those for an ideal gas. The results obtained here enable us to conduct more efficient molecular dynamics simulations such as simulating shock fronts alone for the investigation of the internal structures of liquid shock waves.
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Renardy, Michael. "On Rankine—Hugoniot conditions for Maxwell liquids." Journal of Non-Newtonian Fluid Mechanics 32, no. 1 (January 1989): 69–77. http://dx.doi.org/10.1016/0377-0257(89)85041-4.

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Szabo, A. "An improved solution to the “Rankine-Hugoniot” problem." Journal of Geophysical Research 99, A8 (1994): 14737. http://dx.doi.org/10.1029/94ja00782.

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GAVRILYUK, S. L., and R. SAUREL. "Rankine–Hugoniot relations for shocks in heterogeneous mixtures." Journal of Fluid Mechanics 575 (March 2007): 495–507. http://dx.doi.org/10.1017/s0022112006004496.

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The conservation of mass, momentum and energy are not sufficient to close a system of jump relations for shocks propagating in a heterogeneous mixture of compressible fluids. We propose here a closed set of relations corresponding to a two-stage structure of shock fronts. At the first stage, microkinetic energy due to the relative motion of mixture components is produced at the shock front. At the second stage, this microkinetic energy disappears inducing strong variations in the thermodynamical states that reach mechanical equilibrium. The microkinetic energy produced at the shock front is estimated by using an idea developed earlier for turbulent shocks in compressible fluids. The relaxation zone between the shocked state and the equilibrium state is integrated over a thermodynamic path a justification of which is provided. Comparisons with experiments on shock propagation in a mixture of condensed materials confirm the proposed theory.
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Dissertations / Theses on the topic "Rankine-Hugoniot"

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Rossini, Alex Ferreira. "Leis de conservacão escalar : fórmula explícita e unicidade." Universidade Federal de São Carlos, 2011. https://repositorio.ufscar.br/handle/ufscar/5874.

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We study scalar conservation laws, with the deduction of an explicit formula of a smooth solution with compact support, we also present the behavior of the solution given by the formula when the initial value is zero outside a finite interval. In order to study the uniqueness of a given conservation law under certain hypotheses.
Neste trabalho estudamos leis de conservação escalar, com a dedução de uma fórmula explícita de uma solução suave de suporte compacto, também apresentamos o comportamento da solução dada pela fórmula quando o dado inicial é nulo fora de algum intervalo limitado e por fim estudamos a unicidade para uma dada lei de conservação sob certas hipóteses.
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Kolluru, Ramesh. "Novel, Robust and Accurate Central Solvers for Real, Dense and Multicomponent Gases." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/4667.

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The nonlinear convection terms in the governing equations of inviscid compressible fluid flows are nontrivial for modelling and numerical simulation. The traditional Riemann solvers, which are strongly dependent on the underlying eigen-structure of the governing equations. Extension of the existing methods for generalized Equation of State (EOS), to incorporate real gas effects and for multicomponent fluids, is not straight forward as the eigen-structure can become complicated. Objective of the present work is to develop simple algorithms which are not dependent on the eigen-structure and can tackle easily hyperbolic systems with various equations of state. Central schemes with smart diffusion mechanisms are apt for this purpose. For fi xing the numerical diffusion, the basic ideas of satisfying the Rankine-Hugoniot con- ditions along with generalized Riemann invariants are proposed. Two such interesting algorithms are presented, which capture steady contact discontinuity exactly and have minimum numerical diffusion in smooth regions to avoid numerical instabilities. First, an interesting modi cation of a recently developed central solver (Method of Op- timal Viscosity for Enhanced Resolution of Shocks (MOVERS)), based on enforcing Rankine-Hugoniot jump conditions at the discrete level, is presented. The proposed modi cation avoids the wave-speed correction mechanism required for MOVERS and the modi ed algorithm is termed as MOVERS+. Further, a shock sensor is introduced to choose appropriate numerical diffusion in different regions. The second novel algorithm introduced in this thesis is based on selecting the numeri- cal diffusion by utilizing the generalized Riemann invariants. In this Riemann Invariant based Contact-discontinuty Capturing Algorithm (RICCA), additional numerical diffusion is also introduced based on the scaled speed of sound for robustness. Both the algorithms presented are robust in avoiding shock instabilities, are accurate in capturing grid aligned steady contact discontinuities, do not need wave speed corrections and are independent of eigen-strutures of the underlying hyperbolic systems. These algorithms have been tested with perfect gas EOS, stiffened gas, van der Waals and 5th order (5O) Virial EOS and also multicomponent gases. For multicomponent gases, both mass fraction and -based models have been used and are tested for condi- tions which are known to generate pressure oscillations. The proposed algorithms have also been utilized in simulating dense gas flows, in which the non-classical mixed shock- expansion waves and expansion shocks are physical features, due to a change in the sign of the fundamental derivative. These algorithms perform very well, without needing any modi cations for such dense gas flows. Further these numerical methods are also used to simulate viscous flows.
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Jaisankar, S. "Accurate Computational Algorithms For Hyperbolic Conservation Laws." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/905.

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The numerics of hyperbolic conservation laws, e.g., the Euler equations of gas dynamics, shallow water equations and MHD equations, is non-trivial due to the convective terms being highly non-linear and equations being coupled. Many numerical methods have been developed to solve these equations, out of which central schemes and upwind schemes (such as Flux Vector Splitting methods, Riemann solvers, Kinetic Theory based Schemes, Relaxation Schemes etc.) are well known. The majority of the above mentioned schemes give rise to very dissipative solutions. In this thesis, we propose novel low dissipative numerical algorithms for some hyperbolic conservation laws representing fluid flows. Four different and independent numerical methods which give low diffusive solutions are developed and demonstrated. The first idea is to regulate the numerical diffusion in the existing dissipative schemes so that the smearing of solution is reduced. A diffusion regulator model is developed and used along with the existing methods, resulting in crisper shock solutions at almost no added computational cost. The diffusion regulator is a function of jump in Mach number across the interface of the finite volume and the average Mach number across the surface. The introduction of the diffusion regulator makes the diffusive parent schemes to be very accurate and the steady contact discontinuities are captured exactly. The model is demonstrated in improving the diffusive Local Lax-Friedrichs (LLF) (or Rusanov) method and a Kinetic Scheme. Even when employed together with accurate methods of Roe and Osher, improvement in solutions is demonstrated for multidimensional problems. The second method, a Central Upwind-Biased Scheme (CUBS), attempts to reorganize a central scheme such that information from irrelevant directions is largely reduced and the upwind biased information is retained. The diffusion co-efficient follows a new format unlike the use of maximum characteristic speed in the Local Lax-Friedrichs method and the scheme results in improved solutions of the flow features. The grid-aligned steady contacts are captured exactly with the reorganized format of diffusion co-efficient. The stability and positivity of the scheme are discussed and the procedure is demonstrated for its ability to capture all the features of solution for different flow problems. Another method proposed in this thesis, a Central Rankine-Hugoniot Solver, attempts to integrate more physics into the discretization procedure by enforcing a simplified Rankine-Hugoniot condition which describes the jumps and hence resolves steady discontinuities very accurately. Three different variants of the scheme, termed as the Method of Optimal Viscosity for Enhanced Resolution of Shocks (MOVERS), based on a single wave (MOVERS-1), multiple waves (MOVERS-n) and limiter based diffusion (MOVERS-L) are presented. The scheme is demonstrated for scalar Burgers equation and systems of conservation laws like Euler equations, ideal Magneto-hydrodynamics equations and shallow water equations. The new scheme uniformly improves the solutions of the Local Lax-Friedrichs scheme on which it is based and captures steady discontinuities either exactly or very accurately. A Grid-Free Central Solver, which does not require a grid structure but operates on any random distribution of points, is presented. The grid-free scheme is generic in discretization of spatial derivatives with the location of the mid-point between a point and its neighbor being used to define a relevant coefficient of numerical dissipation. A new central scheme based on convective-pressure splitting to solve for mid-point flux is proposed and many test problems are solved effectively. The Rankine-Hugoniot Solver, which is developed in this thesis, is also implemented in the grid-free framework and its utility is demonstrated. The numerical methods presented are solved in a finite volume framework, except for the Grid-Free Central Solver which is a generalized finite difference method. The algorithms developed are tested on problems represented by different systems of equations and for a wide variety of flow features. The methods presented in this thesis do not need any eigen-structure and complicated flux splittings, but can still capture discontinuities very accurately (sometimes exactly, when aligned with the grid lines), yielding low dissipative solutions. The thesis ends with a highlight on the importance of developing genuinely multidimensional schemes to obtain accurate solutions for multidimensional flows. The requirement of simpler discretization framework for such schemes is emphasized in order to match the efficacy of the popular dimensional splitting schemes.
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Jaisankar, S. "Accurate Computational Algorithms For Hyperbolic Conservation Laws." Thesis, 2008. http://hdl.handle.net/2005/905.

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The numerics of hyperbolic conservation laws, e.g., the Euler equations of gas dynamics, shallow water equations and MHD equations, is non-trivial due to the convective terms being highly non-linear and equations being coupled. Many numerical methods have been developed to solve these equations, out of which central schemes and upwind schemes (such as Flux Vector Splitting methods, Riemann solvers, Kinetic Theory based Schemes, Relaxation Schemes etc.) are well known. The majority of the above mentioned schemes give rise to very dissipative solutions. In this thesis, we propose novel low dissipative numerical algorithms for some hyperbolic conservation laws representing fluid flows. Four different and independent numerical methods which give low diffusive solutions are developed and demonstrated. The first idea is to regulate the numerical diffusion in the existing dissipative schemes so that the smearing of solution is reduced. A diffusion regulator model is developed and used along with the existing methods, resulting in crisper shock solutions at almost no added computational cost. The diffusion regulator is a function of jump in Mach number across the interface of the finite volume and the average Mach number across the surface. The introduction of the diffusion regulator makes the diffusive parent schemes to be very accurate and the steady contact discontinuities are captured exactly. The model is demonstrated in improving the diffusive Local Lax-Friedrichs (LLF) (or Rusanov) method and a Kinetic Scheme. Even when employed together with accurate methods of Roe and Osher, improvement in solutions is demonstrated for multidimensional problems. The second method, a Central Upwind-Biased Scheme (CUBS), attempts to reorganize a central scheme such that information from irrelevant directions is largely reduced and the upwind biased information is retained. The diffusion co-efficient follows a new format unlike the use of maximum characteristic speed in the Local Lax-Friedrichs method and the scheme results in improved solutions of the flow features. The grid-aligned steady contacts are captured exactly with the reorganized format of diffusion co-efficient. The stability and positivity of the scheme are discussed and the procedure is demonstrated for its ability to capture all the features of solution for different flow problems. Another method proposed in this thesis, a Central Rankine-Hugoniot Solver, attempts to integrate more physics into the discretization procedure by enforcing a simplified Rankine-Hugoniot condition which describes the jumps and hence resolves steady discontinuities very accurately. Three different variants of the scheme, termed as the Method of Optimal Viscosity for Enhanced Resolution of Shocks (MOVERS), based on a single wave (MOVERS-1), multiple waves (MOVERS-n) and limiter based diffusion (MOVERS-L) are presented. The scheme is demonstrated for scalar Burgers equation and systems of conservation laws like Euler equations, ideal Magneto-hydrodynamics equations and shallow water equations. The new scheme uniformly improves the solutions of the Local Lax-Friedrichs scheme on which it is based and captures steady discontinuities either exactly or very accurately. A Grid-Free Central Solver, which does not require a grid structure but operates on any random distribution of points, is presented. The grid-free scheme is generic in discretization of spatial derivatives with the location of the mid-point between a point and its neighbor being used to define a relevant coefficient of numerical dissipation. A new central scheme based on convective-pressure splitting to solve for mid-point flux is proposed and many test problems are solved effectively. The Rankine-Hugoniot Solver, which is developed in this thesis, is also implemented in the grid-free framework and its utility is demonstrated. The numerical methods presented are solved in a finite volume framework, except for the Grid-Free Central Solver which is a generalized finite difference method. The algorithms developed are tested on problems represented by different systems of equations and for a wide variety of flow features. The methods presented in this thesis do not need any eigen-structure and complicated flux splittings, but can still capture discontinuities very accurately (sometimes exactly, when aligned with the grid lines), yielding low dissipative solutions. The thesis ends with a highlight on the importance of developing genuinely multidimensional schemes to obtain accurate solutions for multidimensional flows. The requirement of simpler discretization framework for such schemes is emphasized in order to match the efficacy of the popular dimensional splitting schemes.
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Books on the topic "Rankine-Hugoniot"

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D, Scudder Jack, and Goddard Space Flight Center, eds. Fast and optimal solution to the 'Rankine-Hugoniot problem'. Greenbelt, Md: National Aeronautics and Space Administration, Goddard Space Flight Center, 1985.

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Whang, Y. C. Interaction of minor ions with fast and slow shocks: Final report. Washington, D.C: Catholic University of America, Dept. of Mechanical Engineering, 1990.

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Zeitlin, Vladimir. Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0007.

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The chapter contains the mathematical background necessary to understand the properties of RSW models and numerical methods for their simulations. Mathematics of RSW model is presented by using their one-dimensional reductions, which are necessarily’one-and-a-half’ dimensional, due to rotation and include velocity in the second direction. Basic notions of quasi-linear hyperbolic systems are recalled. The notions of weak solutions, wave breaking, and shock formation are introduced and explained on the example of simple-wave equation. Lagrangian description of RSW is used to demonstrate that rotation does not prevent wave-breaking. Hydraulic theory and Rankine–Hugoniot jump conditions are formulated for RSW models. In the two-layer case it is shown that the system loses hyperbolicity in the presence of shear instability. Ideas of construction of well-balanced (i.e. maintaining equilibria) shock-resolving finite-volume numerical methods are explained and these methods are briefly presented, with illustrations on nonlinear evolution of equatorial waves.
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Book chapters on the topic "Rankine-Hugoniot"

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Needham, Charles E. "The Rankine–Hugoniot Relations." In Blast Waves, 9–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-05288-0_3.

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Needham, Charles E. "The Rankine-Hugoniot Relations." In Blast Waves, 9–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65382-2_3.

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Després, B. "The Weak Rankine Hugoniot Inequality." In Hyperbolic Problems: Theory, Numerics, Applications, 439–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75712-2_41.

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Prunty, Seán. "Conditions Across the Shock: The Rankine-Hugoniot Equations." In Shock Wave and High Pressure Phenomena, 81–109. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02565-6_3.

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Prunty, Seán. "Conditions Across the Shock: The Rankine-Hugoniot Equations." In Shock Wave and High Pressure Phenomena, 89–130. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63606-7_3.

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Bui-Thanh, Tan. "From Rankine-Hugoniot Condition to a Constructive Derivation of HDG Methods." In Lecture Notes in Computational Science and Engineering, 483–91. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19800-2_45.

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Dewey, John M. "The Rankine–Hugoniot Equations: Their Extensions and Inversions Related to Blast Waves." In Shock Wave and High Pressure Phenomena, 17–35. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70831-7_2.

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Shelkovich, V. M. "Concept of Delta-shock Type Solutions to Systems of Conservation Laws and the Rankine–Hugoniot Conditions." In Pseudo-Differential Operators, Generalized Functions and Asymptotics, 297–305. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_16.

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"Hugoniot-Rankine Conditions." In Physicochemical Fluid Dynamics in Porous Media, 349–50. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2018. http://dx.doi.org/10.1002/9783527806577.app5.

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William, Forman A. "Rankine-Hugoniot Relations." In Combustion Theory, 19–37. CRC Press, 2018. http://dx.doi.org/10.1201/9780429494055-2.

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Conference papers on the topic "Rankine-Hugoniot"

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Kennel, Charles F. "The magnetohydrodynamic Rankine-Hugoniot relations." In Advances in plasma physics. AIP, 1994. http://dx.doi.org/10.1063/1.46750.

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Sano, Yukio, Tomokazu Sano, Mark Elert, Michael D. Furnish, Ricky Chau, Neil Holmes, and Jeffrey Nguyen. "UNSTEADY STATE RANKINE-HUGONIOT JUMP CONDITIONS." In SHOCK COMPRESSION OF CONDENSED MATTER - 2007: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter. AIP, 2008. http://dx.doi.org/10.1063/1.2833027.

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Saeks, Richard, and John Murray. "Analysis of the Modified Rankine Hugoniot Equations." In 34th AIAA Plasmadynamics and Lasers Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-4180.

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Dasgupta, B. "Magnetohydrodynamics of Shocks with Reflected Particles: Rankine-Hugoniot Relations." In THE PHYSICS OF COLLISIONLESS SHOCKS: 4th Annual IGPP International Astrophysics Conference. AIP, 2005. http://dx.doi.org/10.1063/1.2032676.

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Lancellotti, Carlo, and Yubei Yue. "Corrections to the Rankine-Hugoniot conditions for curved shock waves." In PROCEEDINGS OF THE 29TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902576.

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Shelkovich, V. M. "Delta-shocks, the Rankine-Hugoniot conditions, and singular superposition of distributions." In Proceedings of the International Seminar Days on Diffraction, 2004. IEEE, 2004. http://dx.doi.org/10.1109/dd.2004.186028.

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Lee, J. W., W. S. Ohm, and W. Shim. "Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations." 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/10.1063/1.4934448.

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PFITZNER, M. "A 3-D non-equilibrium shock-fitting algorithm using effective Rankine-Hugoniot relations." In 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-1467.

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Baeza, Antonio, Carlos Castro, Francisco Palacios, and Enrique Zuazua. "2D Euler Shape Design on Non-Regular Flows Using Adjoint Rankine-Hugoniot Relations." In 46th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-171.

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SREEDHAR, V. V. "CONSERVATION LAWS IN FLUID DYNAMICS AND SELF-DUALITY OF RANKINE-HUGONIOT SHOCK CONDITIONS." In Proceedings of the 3rd International Symposium. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702340_0047.

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Reports on the topic "Rankine-Hugoniot"

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Shaw, B. W. A Rankine-Hugoniot Emulating (Density vs. Velocity) Relationship for CFD Usage Within an Inviscid Shock Wave. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada251672.

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