Numerical solution of the propagation of cylindrical shock waves in a magnetic field

1987 ◽  
Vol 27 (6) ◽  
pp. 879-883 ◽  
Author(s):  
N. A. Kudryashov ◽  
S. S. Kucherenko ◽  
A. I. Poberezhnyi
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Numerical Solution ◽  
Cylindrical Shock Waves

scholarly journals Converging Cylindrical Symmetric Shock Waves in a Real Medium with a Magnetic Field

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1177 ◽  
Author(s):  
Munesh Devi ◽  
Rajan Arora ◽  
Mustafa M. Rahman ◽  
Mohd Junaid Siddiqui
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Inertial Confinement Fusion ◽  
Matrix Form ◽  
Ideal Medium ◽  
Group Theoretic Method ◽  
Real Medium ◽  
Cylindrical Shock Waves

The topic “converging shock waves” is quite useful in Inertial Confinement Fusion (ICF). Most of the earlier studies have assumed that the medium of propagation is ideal. However, due to very high temperature at the axis of convergence, the effect of medium on shock waves should be taken in account. We have considered a problem of propagation of cylindrical shock waves in real medium. Magnetic field has been assumed in axial direction. It has been assumed that electrical resistance is zero. The problem can be represented by a system of hyperbolic Partial Differential Equations (PDEs) with jump conditions at the shock as the boundary conditions. The Lie group theoretic method has been used to find solutions to the problem. Lie’s symmetric method is quite useful as it reduces one-dimensional flow represented by a system of hyperbolic PDEs to a system of Ordinary Differential Equations (ODEs) by means of a similarity variable. Infinitesimal generators of Lie’s group transformation have been obtained by invariant conditions of the governing and boundary conditions. These generators involves arbitrary constants that give rise to different possible cases. One of the cases has been discussed in detail by writing reduced system of ODEs in matrix form. Cramer’s rule has been used to find the solution of system in matrix form. The results are presented in terms of figures for different values of parameters. The effect of non-ideal medium on the flow has been studied. Guderley’s rule is used to compute similarity exponents for cylindrical shock waves, in gasdynamics and in magnetogasdynamics (ideal medium), in order to set up a comparison with the published work. The computed values are very close to the values in published articles.

scholarly journals The Propagation of Hydromagnetic Cylindrical Shock Waves in Weak Magnetic Field, With A Self-Gravitating Gas

2021 ◽  
pp. 311-323
Author(s):  
Dr. Sarvesh Chandra Yadav
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Shock Front ◽  
Initial Density ◽  
Analytical Formula ◽  
Weak Shock ◽  
Propagation Distance ◽  
Ideal Gas ◽  
Flow Variables ◽  
Cylindrical Shock Waves

<p>The effects of overtaking disturbances behind the flow on the propagation of diverging cylindrical shock Waves through an ideal gas in presence of a magnetic field having =constant=  and an Initial density distribution  where  is a constant,  is the density at the plane / exes of symmetry: The analytical formula for flow variables representing both the position form viz; weak and strong cases at shock waves have been obtained. Their numerical estimates at permissible shock front locations have been obtained.</p> <p>There numerical estimates at permissible shock front location's have been Calculated and compared with earlier result describing in Free Propagation through figures. After inclusion of E.O.D. noted that there is no change at flow variable with parameters and . However, the trends of variation with propagation distance r, for shock strength, shock velocity and particle velocity are not change in case of weak shock with work Magnetic field<strong>(wswmf).</strong></p>

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