Similarity method for the study of strong shock waves in magnetogasdynamics

Abstract

In this paper, a non-dimensional unsteady adiabatic flow of a plane or cylindrical strong shock wave propagating in plasma is studied. The plasma is assumed to be an ideal gas with infinite electrical conductivity permeated by a transverse magnetic field. A self-similar solution of the problem is obtained in terms of density, velocity and pressure in the presence of magnetic field. We use the method of Lie group invariance to determine the class of self-similar solutions. The arbitrary constants, occurring in the expressions of the generators of the local Lie group of transformations, give rise to different cases of possible solutions with a power law, exponential or logarithmic shock paths. A particular case of the collapse of an imploding shock is worked out in detail. Numerical calculations have been performed to obtain the similarity exponents and the profiles of flow variables. Our results are found in good agreement with the known results. All computational work is performed by using software package MATHEMATICA.

Propagation of shock waves in a non‐ideal gas under the action of magnetic field

“…Many researchers have worked to better understand the dynamics of shock waves with the magnetic field effects. The works of Arora et al, 20 Jena, 21 Menon and Sharma, 22 Nath and Singh, 23,24 Pandey and Pathak, 25 Pandey et al, 26 Ram et al, 27 Singh and Arora, 28 Singh et al, 29 Siddiqui et al, 30 Singh et al, 31,32 and Vishwakarma and Yadav 33 are worth mentioning in this context.…”

“…where W (j ) , P (j ) , (j ) , and I (j ) are the functions of r only, and j = 0, 1, 2, … . Now, using Equation (20) in Equation 19, we obtain J = J 0 (1…”

“…To obtain the ODEs governing the functions W (j ) , P (j ) , (j ) , and I (j ) (j = 0, 1, 2, … ), we use the Equations (20) and (27) in Equation 14and compare the coefficients of like powers of on both the sides. On comparing the coefficients of zeroth power of , we get (W (0) − r) (0) r…”

Propagation of Blast Waves in a Non-Ideal Magnetogasdynamics

“…The fundamental equations which govern unsteady planar (m = 0) or cylindrically (m = 1) symmetric flow in a non-ideal gas in the presence of transverse magnetic field can be expressed as [12,21]…”

“…Many research groups have worked afterwards on the topic to better understand the dynamics of shock waves in a magnetic field. Among the recent research on the topic, we wish to mention the work of Arora et al [12], Siddiqui et al [13], Singh et al [14,15], and Pandey et al [16]. Menon and Sharma [17] studied the flattening and steepening of the characteristics wave fronts in an ideal medium with magnetic field.…”