https://doi.org/10.1140/epjp/s13360-025-06408-8
Regular Article
Converging cylindrical shock waves in van der Waals gas with dust particles under the effect of magnetic field
Department of Applied Mathematics and Scientific Computing, Indian Institute of Technology Roorkee, 247667, Roorkee, India
Received:
15
March
2025
Accepted:
6
May
2025
Published online:
28
May
2025
In this paper, by using the Lie group of transformation, a complete range of self-similar solutions is obtained for a quasi-linear hyperbolic system of partial differential equations which describes a problem of imploding cylindrical shock waves in a van der Waals dusty gas through the axial magnetic field. The necessary conditions for the existence of similarity solutions for strong shocks are discussed. The collapse of imploding (converging) cylindrical shocks is also studied and the impact of non-ideal parameters, the relative specific heat, the ratio of the density of solid particles to the initial density of the gas, the mass concentration of dust particles and shock Cowling number on shock evolution are also discussed in detail and depicted graphically.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
