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Similarity solutions for magnetogasdynamic cylindrical shock wave in rotating non-ideal gas using Lie group theoretic method

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Abstract

The propagation of magnetogasdynamic cylindrical shock wave in rotating non-ideal gas under adiabatic flow condition, using Lie group of transformation method is investigated. The density is assumed to be constant, and magnetic field and azimuthal fluid velocity are assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the Local Lie group of transformations bring about two different cases of solutions, i.e. one with shock front expanding as power law and the other with shock front expanding as exponential law. Numerical solutions are obtained for both the cases of power-law and exponential-law shock paths. Distribution of magnetogasdynamical quantities is illustrated through figures. It is obtained that reduced azimuthal fluid velocity decreases, reduced radial fluid velocity increases, and reduced magnetic field decreases, attains the minimum and then increases for both cases of power-law and exponential-law shock paths as we move inwards from the shock front to the axis of symmetry. Reduced density decreases in the case of power-law shock path whereas it increases in the case of exponential law shock path. Also it is obtained that shock strength decreases with increase in value of adiabatic exponent, Alfven-Mach number or gas non-idealness parameter, whereas it increases due to increase in ambient azimuthal fluid velocity exponent.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh, 211004, India

    Sumeeta Singh

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Singh, S. Similarity solutions for magnetogasdynamic cylindrical shock wave in rotating non-ideal gas using Lie group theoretic method. J Eng Math 131, 5 (2021). https://doi.org/10.1007/s10665-021-10169-5

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