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Converging strong shock waves in magnetogasdynamics under isothermal condition

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Abstract

The similarity solutions to the problem of cylindrically symmetric strong shock waves in an ideal gas with a constant azimuthal magnetic field are presented. The flow behind the shock wave is assumed to spatially isothermal rather than adiabatic. We use the method of Lie group invariance to determine the possible class of self-similar solutions. Infinitesimal generators of Lie group transformations are determined by using the invariance surface conditions to the system and on the basis of arbitrary constants occurring in the expressions for the generators, four different possible cases of the solutions are reckoned and we observed that only two out of all possibilities hold self-similar solutions, one of which follows the power law and another follows the exponential law. To obtain the similarity exponents numerical calculations have been performed and comparison is made with the existing results in the literature. The flow patterns behind the shock are analyzed graphically.

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Acknowledgements

The first author Antim Chauhan has acknowledged the research support from “University Grant Commission (Govt of India)” (Sr. No. 2121541039 with Ref No. 20/12/2015 (ii)EU-V).

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Authors and Affiliations

  1. Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Antim Chauhan & Rajan Arora

  2. Department of Mathematics, Amity Institute of Applied Science, Amity University Noida, 201301, India

    Amit Tomar

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  1. Antim Chauhan
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  2. Rajan Arora
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  3. Amit Tomar
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Correspondence to Rajan Arora.

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Chauhan, A., Arora, R. & Tomar, A. Converging strong shock waves in magnetogasdynamics under isothermal condition. Ricerche mat 71, 297–313 (2022). https://doi.org/10.1007/s11587-020-00491-y

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