scholarly journals Propagation of Shock Waves in a Polytrope with a Toroidal Magnetic Field. I. Simplified Solution of Differential Equations

1969 ◽  
Vol 22 (5) ◽  
pp. 589
Author(s):  
NK Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Shock Waves ◽  
Differential Equations ◽  
Toroidal Magnetic Field ◽  
Spherical Shock Wave ◽  
Simplified Solution ◽  
Spherical Shock

The propagation of an initially spherical shock wave in a polytrope with a magnetic field has been studied. The model chosen for the purpose was that of a poly trope with a toroidal magnetic field given previously by Sinha. Butler's method has been extended to transform the set of governing partial differential equations into a set of ordinary differential equations involving derivatives in the direction of propagation of the shock element at any point. An approximate solution is obtained and the effect of the toroidal magnetic field on the geometry of the front as well as on the effects brought about by the shock is discussed.

scholarly journals Propagation of Shock Waves in a Polytrope with a Toroidal Magnetic Field. II. Solution of Complete Differential Equations

1969 ◽  
Vol 22 (5) ◽  
pp. 605
Author(s):  
NK Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Differential Equations ◽  
Toroidal Magnetic Field ◽  
Initial Values ◽  
Made In

The differential equations for the shock parameters along shock rays in the case of propagation of a spherically developed shock wave in a polytrope with a toroidal magnetic field, obtained in Part I, have been integrated numerically for a particular set of initial values. The results are compared with the corresponding results in Part I obtained by neglecting certain small terms and it is found that the effect of this omission is not significant. This substantiates the results and justifies the simplification made in Part 1.

One-dimensional spherical shock waves in an interstellar dusty gas clouds

2021 ◽  
Vol 76 (5) ◽  
pp. 417-425
Author(s):  
Astha Chauhan ◽  
Kajal Sharma
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Differential Equations ◽  
Shock Propagation ◽  
Dusty Gas ◽  
Shock Strength ◽  
Efficient System ◽  
One Dimensional ◽  
Arbitrary Strength ◽  
Spherical Shock

Abstract A system of partial differential equations describing the one-dimensional motion of an inviscid self-gravitating and spherical symmetric dusty gas cloud, is considered. Using the method of the kinematics of one-dimensional motion of shock waves, the evolution equation for the spherical shock wave of arbitrary strength in interstellar dusty gas clouds is derived. By applying first order truncation approximation procedure, an efficient system of ordinary differential equations describing shock propagation, which can be regarded as a good approximation of infinite hierarchy of the system. The truncated equations, which describe the shock strength and the induced discontinuity, are used to analyze the behavior of the shock wave of arbitrary strength in a medium of dusty gas. The results are obtained for the exponents from the successive approximation and compared with the results obtained by Guderley’s exact similarity solution and characteristic rule (CCW approximation). The effects of the parameters of the dusty gas and cooling-heating function on the shock strength are depicted graphically.

Finite Mach number spherical shock wave, application to shock ignition

2013 ◽  
Vol 20 (8) ◽  
pp. 082702 ◽  
Author(s):  
A. Vallet ◽  
X. Ribeyre ◽  
V. Tikhonchuk
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Spherical Shock Wave ◽  
Spherical Shock ◽  
Shock Ignition

Simulation of Interaction between a Spherical Shock Wave and a Layer of Granular Material in a Conical Shock Tube

2021 ◽  
Vol 15 (4) ◽  
pp. 685-690
Author(s):  
S. V. Khomik ◽  
I. V. Guk ◽  
A. N. Ivantsov ◽  
S. P. Medvedev ◽  
E. K. Anderzhanov ◽  
...  
Keyword(s):  
Shock Wave ◽  
Granular Material ◽  
Shock Tube ◽  
Spherical Shock Wave ◽  
Conical Shock ◽  
Spherical Shock

Spherical waves in a simple locking medium

1964 ◽  
Vol 54 (2) ◽  
pp. 737-754
Author(s):  
Sathyanarayana Hanagud
Keyword(s):  
Shock Wave ◽  
Stress Distribution ◽  
Mechanical Behavior ◽  
Spherical Cavity ◽  
Shear Resistance ◽  
Finite Deformations ◽  
Spherical Shock Wave ◽  
Spherical Waves ◽  
Spherical Shock ◽  
Elastic Shear

ABSTRACT The mechanical behavior of some types of soils can be idealized by that of a “Locking Solid.” This paper investigates the spherical shock wave and the stress distribution behind the wave in a simple locking solid due to a sudden explosion at the surface of a small spherical cavity. The cases of infinitesimal and finite deformations are considered. The effect of an elastic shear resistance and the consequent phenomenon of “unlocking” are also studied.

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