Similarity solutions for magnetogasdynamic shock waves in a rotating ideal gas using the Lie group-theoretic method. (English) Zbl 1479.35039
Summary: The propagation of a cylindrical shock wave under the influence of an azimuthal magnetic field in a rotating medium for adiabatic flow conditions is investigated using the Lie group transformation method. The density, magnetic field, and azimuthal and axial fluid velocities are assumed to vary in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the local Lie group of transformations bring about different cases of solutions, i.e., with a power-law shock path, with an exponential-law shock path, and a particular case of a power-law shock path. Numerical solutions are obtained in the case of a power-law shock path and exponential-law shock path. The distributions of gasdynamical quantities are discussed based on figures. The effects of varying the values of the adiabatic exponent \(\gamma \), Alfven-Mach number \(M_\text{A}^{-2} \), ambient azimuthal fluid velocity variation index \(\lambda_1\), and ambient density variation index \(\phi\) on the flow variables and shock strength are studied. With an increase in the adiabatic exponent or the strength of the magnetic field, the shock strength decreases. However, an increase in the ambient density variation index or ambient azimuthal fluid velocity variation index results in an increase in the shock strength. The numerical calculations are carried out using Mathematica software.
MSC:
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35C06 | Self-similar solutions to PDEs |
| 35L60 | First-order nonlinear hyperbolic equations |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
Software:
MathematicaReferences:
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