Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas

Pandey, Manoj; Sharma, V. D.

doi:10.1016/j.wavemoti.2006.12.002

Cited by 72 publications

(18 citation statements)

References 14 publications

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“…Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas was discussed in Ref. [13]. Similarity solutions for three-dimensional Euler equations using symmetry analysis have been discussed by Sekhar and Sharma [14] .…”

Section: Introductionmentioning

confidence: 92%

Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

Sekhar

Bira

2015

Appl. Math. Mech.-Engl. Ed.

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In the present paper, Lie group symmetry method is used to obtain some exact solutions for a hyperbolic system of partial differential equations (PDEs), which governs an isothermal no-slip drift-flux model for multiphase flow problem. Those symmetries are used for the governing system of equations to obtain infinitesimal transformations, which consequently reduces the governing system of PDEs to a system of ODEs. Further, the solutions of the system of ODEs which in turn produces some exact solutions for the PDEs are presented. Finally, the evolutionary behavior of weak discontinuity is discussed.

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Section: Introductionmentioning

confidence: 92%

Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

Sekhar

Bira

2015

Appl. Math. Mech.-Engl. Ed.

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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: 93%

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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“…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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Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas

Cited by 72 publications

References 14 publications

Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

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

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