Lie group of invariance technique for analyzing propagation of strong shock wave in a rotating non‐ideal gas with azimuthal magnetic field

Abstract

In this manuscript, the propagation of strong shock wave in a non-ideal gas in the presence of azimuthal magnetic field with rotational effect is examined by using the Lie group of invariance technique with an assumption of uniform density in the undisturbed medium, whereas the azimuthal component of the fluid velocity and magnetic field are supposed to vary. The main advantage of this method is to reduce the number of independent variables by one. We obtained a special class of self-similar solutions to the problem, and the flow profiles are depicted graphically behind the shock followed by a brief discussion on the behavior of solutions through graphs. The effects of variation in non-ideal parameter, adiabatic index of the gas, Alfven-Mach number and ambient azimuthal velocity exponent on the flow variables are presented. All numerical calculations have been done using the "Mathematica"software.

The propagation of strong cylindrical shock wave in a rotating axisymmetric non‐ideal gas with radiation heat flux

“…Unfortunately, to the best of our knowledge, there are no experimental results that can be used as a benchmark for the presently considered problem. However, the obtained results in Figures 2,4, and 5 match well with the existing graphs of Yadav et al [8] for non-radiating gas (S = 0). The following conclusions can be made from Table 1 and Figures 2-5:…”

“…We obtain the similarity solutions using these infinitesimal generators. The group-theoretic method and its applications in various fields can be found in the literature [1][2][3][4][5][6][7][8][9][10].…”

Lie symmetries, solitary wave solutions, and conservation laws of coupled KdV‐mKdV equation for internal gravity waves

“…This section introduces conservation laws for KdV-mKdV equation associated with Lie symmetry analysis [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The adjoint equation and Lagrangian operator are determined using Noether's theorem.…”

“…Therefore, nonlinear partial differential equations (NPDEs) play a major role in modeling of these natural waves and several wave phenomena as well. The massive applications of NPDEs can be seen in various fields of mathematical sciences, biological sciences, nonlinear optics, electromagnetic theory, quantum theory, optical fiber, plasma physics, heat transfer, fluid dynamics, and so forth [1‐32,33,34]. The NPDEs are difficult to handle with traditional methods, so a large number of methods such as Darboux transformations [1], Fan's subequation method [3], extended mapping method [4], sub‐ODE method [5], extended tanh method [6], amplitude ansatz method [7], WTC truncation method [8], nonlocal symmetry method [9], and similarity transformation method [10–34] are evolved to derive exact solutions.…”

Detonation in van der Waals Gas

“…The group invariance method is used to analyze the propagation of a strong shock wave in a rotating non-ideal gas with an azimuthally magnetic field [6][7][8]. The effect of changing the gas non-ideality parameter, the adiabatic index, the Mach number, and the environmental azimuth velocity index on the shock wave strength and flow parameters is shown.…”