Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength

Mentrelli, Andrea; Ruggeri, Tommaso; Sugiyama, Masaru; Zhao, Nanrong

doi:10.1016/j.wavemoti.2007.09.005

Cited by 44 publications

(8 citation statements)

References 19 publications

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“…A further contributions to the study of characteristic shocks (see, Boillat and Ruggeri [5]) and wave interactions which enable the evaluation of reflected and transmitted wave amplitudes when the discontinuity wave encounters a characteristic shock may be found in the paper of Boillat and Ruggeri [6]. The application of this work, to interaction with a shock, has been carried out by Ruggeri [7], Virgopia and Ferraioli [8], Radha et al [9], Pandey and Sharma [10], Pandey et al [11] and Mentrelli et al [12], in various fields. It is a known fact that the shock undergoes an acceleration jump as a consequence of an interaction with the a weak wave; this fact was accounted for in the work of Brun [2] and Boillat and Ruggeri [6].…”

Section: Introductionmentioning

confidence: 89%

Group theoretic method for analyzing interaction of a discontinuity wave with a strong shock in an ideal gas

Pandey

2009

Z. Angew. Math. Phys.

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A group theoretic method is used to obtain an exact particular solution to the system of partial differential equations, describing one-dimensional unsteady planar, cylindrically and spherically symmetric motions in an ideal gas, involving shock waves. It is interesting to remark that the exact solution obtained here is precisely the blast wave solution obtained earlier using a different method of approach. Further, the evolution of a discontinuity wave and its interaction with the strong shock are studied within the state characterized by the exact particular solution. The properties of reflected and transmitted waves and the jump in the shock acceleration are completely characterized, and certain observations are noted in respect to their contrasting behavior. (2000). 35L67 · 76L05. Mathematics Subject Classification

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Section: Introductionmentioning

confidence: 89%

Group theoretic method for analyzing interaction of a discontinuity wave with a strong shock in an ideal gas

Pandey

2009

Z. Angew. Math. Phys.

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“…Let us consider that the C 1 discontinuity is propagating along the characteristic curve determined by dx/dt = λ (1) originating from the point (x 0 , t 0 ), then the transport equation for the C 1 discontinuity is given by (see [19][20][21] and [22])…”

Section: Evolution Of the Weak Discontinuitymentioning

confidence: 99%

Evolution of Weak Discontinuities in Non-ideal Magnetogasdynamic Equations

Pandey

2015

Int. J. Appl. Comput. Math

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In this paper classical Lie group of transformations are used to obtain an exact particular solution to the equations of non-ideal magnetogasdynamics, which exhibits space-time dependence. Appropriate canonical variables are characterized that transform the governing system to an equivalent autonomous form, the autonomous system is solved explicitly to obtain exact particular solution of the original system. The particular solution to the governing system, which exhibits space-time dependence, is used to study the evolutionary behaviour of the weak discontinuities.

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“…For a clear understanding one may refer the fundamental works carried out in [9][10][11][12][13]. Mentrelli et al [14], taking into consideration a perfect gas, studied the interaction between a shock and an acceleration wave with varying shock strength. Many more results have been concluded using the theory in different material media [15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Interaction of a Singular Surface with a Characteristic Shock in a Relaxing Gas with Dust Particles

Mittal

Jena

2019

Zeitschrift Für Naturforschung A

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A system of hyperbolic differential equations outlining one-dimensional planar, cylindrical symmetric and spherical symmetric flow of a relaxing gas with dust particles is considered. Singular surface theory used to study different aspects of wave propagation and its culmination to the steepened form. The evolutionary behavior of the characteristic shock is studied. A particular solution of the governing system of equations is used to discuss the steepened wave form, characteristic shock and their interaction. The results of the interaction between the steepened wave front and the characteristic shock using the general theory of wave interaction are discussed. Also, the influence of relaxation and dust parameters on the steepened wave front, the formation of a characteristic shock, reflected and transmitted waves after interaction and a jump in shock acceleration are investigated.

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Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength

Cited by 44 publications

References 19 publications

Group theoretic method for analyzing interaction of a discontinuity wave with a strong shock in an ideal gas

Group theoretic method for analyzing interaction of a discontinuity wave with a strong shock in an ideal gas

Evolution of Weak Discontinuities in Non-ideal Magnetogasdynamic Equations

Interaction of a Singular Surface with a Characteristic Shock in a Relaxing Gas with Dust Particles

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