Convergence of Strong Shock in a Van der Waals Gas

Arora, Rajan; Sharma, V. D.

doi:10.1137/050634402

Cited by 53 publications

(13 citation statements)

References 5 publications

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“…C 0 = 0 refers to the phenomena under consideration in gas dynamics with ideal or non-ideal conditions (without magnetic field). The computed values for the similarity exponent match well with earlier values obtained by Arora and Sharma [27]. Furthermore, it is observed that, as we move towards the higher values of the parameter C 0 , the obtained values of δ starts decaying which in turns reduce the velocity of shock as shock moves to axis of convergence.…”

Section: Numerical Results and Discussionsupporting

confidence: 88%

“…We are searching for that value of δ for which the determinant ∆ 1 vanishes at Z = 0. We perform these numerical calculations for m = 1 with different values of C 0 , b and γ, and obtain the corresponding values of similarity exponent δ, which is shown in Table 1, which also depicts the comparison with the corresponding values of δ obtained by Guderley's rule and Arora and Sharma [27]. It can be seen that the computed results match well with these results.…”

Section: Numerical Results and Discussionsupporting

confidence: 59%

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Converging Cylindrical Symmetric Shock Waves in a Real Medium with a Magnetic Field

et al. 2019

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The topic "converging shock waves" is quite useful in Inertial Confinement Fusion (ICF). Most of the earlier studies have assumed that the medium of propagation is ideal. However, due to very high temperature at the axis of convergence, the effect of medium on shock waves should be taken in account. We have considered a problem of propagation of cylindrical shock waves in real medium. Magnetic field has been assumed in axial direction. It has been assumed that electrical resistance is zero. The problem can be represented by a system of hyperbolic Partial Differential Equations (PDEs) with jump conditions at the shock as the boundary conditions. The Lie group theoretic method has been used to find solutions to the problem. Lie's symmetric method is quite useful as it reduces one-dimensional flow represented by a system of hyperbolic PDEs to a system of Ordinary Differential Equations (ODEs) by means of a similarity variable. Infinitesimal generators of Lie's group transformation have been obtained by invariant conditions of the governing and boundary conditions. These generators involves arbitrary constants that give rise to different possible cases. One of the cases has been discussed in detail by writing reduced system of ODEs in matrix form. Cramer's rule has been used to find the solution of system in matrix form. The results are presented in terms of figures for different values of parameters. The effect of non-ideal medium on the flow has been studied. Guderley's rule is used to compute similarity exponents for cylindrical shock waves, in gasdynamics and in magnetogasdynamics (ideal medium), in order to set up a comparison with the published work. The computed values are very close to the values in published articles.Raizer [3] have given simple scaling arguments to obtain similarity solutions with an illustration of self-similar or invariant nature of the scaled solutions. Furthermore, the great application of their work is given by Barenblatt [4], giving a clear explanation of the nature of invariant solutions of the first and second kind.A large number of natural phenomena [5][6][7], magnetized stellar winds, shapes of planetary nebulae, galactic winds, complex filamentary structures in molecular clouds, synchrotron radiation from supernova remnants, gamma-ray bursts, dynamo effects in stars, galaxies and galaxy clusters, structure and interaction of supershells as well as other interesting problems all have important roles in magnetic field. Due to its theoretical and practical importance in the variety of astrophysical situations, plasma physics, nuclear science and engineering physics, analysis of magnetogasdynamics has received more attention from researchers in the fields ranging from condensed matter to gas dynamics. Lie's approach is applied to estimate the structure of strong imploding shock waves. Guderley [8], Zeldovich and Raizer [3], Sedov [2], Korobeinikov [9] and Arora et al. [10], etc. studied the imploding shock waves and contributed remarkably in this field. Steeb [11] has applied a group...

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Section: Numerical Results and Discussionsupporting

confidence: 88%

Section: Numerical Results and Discussionsupporting

confidence: 59%

Converging Cylindrical Symmetric Shock Waves in a Real Medium with a Magnetic Field

et al. 2019

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“…The propagation of blast waves establishes a problem of great interest to researchers in a variety of fields such as astrophysics, nuclear science, plasma physics and geophysics. A number of analytical solutions for the blast wave propagation have been obtained by Rogers (1957), Sakurai (1953Sakurai ( , 1954, Madhumita andSharma (2003, 2004), Arora and Sharma (2006), Sedov (1959), Lin (1954) and Taylor (1950aTaylor ( , 1950b. Anisimov and Spiner (1972) studied the problem of point explosion in a non-ideal gas by taking the equation of state in a simplified form to describe the behavior of the medium.…”

Section: Introductionmentioning

confidence: 99%

Quasi-similar solution of the strong shock wave problem in non-ideal gas dynamics

Singh

Ram

Singh

2011

Astrophys Space Sci

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The quasisimilar theory is used to investigate the solution of the blast wave problem with generalized geometries in a non-ideal gas satisfying the equation of state of the Van der Waals type. Here it is assumed that the distribution of normalized velocity, pressure and density are nearly similar in the narrow range of the shock strength. A comparison between approximate analytical solution and numerical solution of the problem is presented for the cylindrical geometry. The numerical solutions are presented for the generalized geometry in a non-ideal gas. It is also assessed as to how the non-idealness of the gas affects the behavior of the flow parameters.

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“…There has been widespread interest in the nonlinear wave phenomena. The work of Whitham [28], Moodie et al [18], He and Moodie ([9,10]), Shtaras [27], Kalyakin [13], Krylovas and Čiegis ( [14,15]), Sharma and Radha [24], Sharma and Srinivasan [25], Sharma and Arora [23], Arora and Sharma [3], and Arora ( [1,2]) is worth mentioning in the context of nonlinear wave propagation in gas dynamic media.…”

Section: Introductionmentioning

confidence: 99%

Asymptotical Solutions for a Vibrationally Relaxing Gas

Arora

2009

Mathematical Modelling and Analysis

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Abstract. Using the weakly non-linear geometrical acoustics theory, we obtain the small amplitude high frequency asymptotic solution to the basic equations governing one dimensional unsteady planar, spherically and cylindrically symmetric flow in a vibrationally relaxing gas with Van der Waals equation of state. The transport equations for the amplitudes of resonantly interacting waves are derived. The evolutionary behavior of non-resonant wave modes culminating into shock waves is also studied.

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Convergence of Strong Shock in a Van der Waals Gas

Cited by 53 publications

References 5 publications

Converging Cylindrical Symmetric Shock Waves in a Real Medium with a Magnetic Field

Converging Cylindrical Symmetric Shock Waves in a Real Medium with a Magnetic Field

Quasi-similar solution of the strong shock wave problem in non-ideal gas dynamics

Asymptotical Solutions for a Vibrationally Relaxing Gas

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