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<p>The Lie group analysis method is employed to obtain the similarity solutions for shock waves in a&#xa0;low conducting rotating non-ideal gas having axial and azimuthal magnetic inductions for cylindrical geometry. The governing partial differential equations representing the physical scenario are converted into ordinary differential equations using the transformations obtained by the Lie group theoretic method. For the existence of a&#xa0;similarity solution, the ambient medium must have a&#xa0;constant initial density. The initial axial and azimuthal magnetic inductions are determined, which follow the power law. The 4‑th order Runge–Kutta technique is employed to solve the derived set of ordinary differential equations. We have examined the impacts of variations in the adiabatic index, non-idealness parameter, magnetic Reynolds number, axial, and azimuthal Cowling numbers on the strength of the shock along with the flow variables behind the shock front in the flow field region. The analysis reveals that the strength of the shock reduces with an increase in the adiabatic index, magnetic Reynolds number, non-idealness parameter, azimuthal and axial Cowling numbers, and rotational parameter.</p>

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Similarity analysis for cylindrical shock wave in a low conducting rotating non-ideal gas in the presence of axial and azimuthal magnetic inductions using the Lie group theoretic method

  • 期刊论文

  • 发表日期：

    2026年4月14日

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  • A. Ghosh,
  • G. Nath

摘要

The Lie group analysis method is employed to obtain the similarity solutions for shock waves in a low conducting rotating non-ideal gas having axial and azimuthal magnetic inductions for cylindrical geometry. The governing partial differential equations representing the physical scenario are converted into ordinary differential equations using the transformations obtained by the Lie group theoretic method. For the existence of a similarity solution, the ambient medium must have a constant initial density. The initial axial and azimuthal magnetic inductions are determined, which follow the power law. The 4‑th order Runge–Kutta technique is employed to solve the derived set of ordinary differential equations. We have examined the impacts of variations in the adiabatic index, non-idealness parameter, magnetic Reynolds number, axial, and azimuthal Cowling numbers on the strength of the shock along with the flow variables behind the shock front in the flow field region. The analysis reveals that the strength of the shock reduces with an increase in the adiabatic index, magnetic Reynolds number, non-idealness parameter, azimuthal and axial Cowling numbers, and rotational parameter.