Similarity method for the study of strong shock waves in magnetogasdynamics
1 Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Saharanpur Campus, Saharanpur 247001, UP, India
2 Department of Mathematics, Zakir Husain Delhi College, University of Delhi, Delhi 110002, Delhi, India
Boundary Value Problems 2014, 2014:142 doi:10.1186/s13661-014-0142-2Published: 11 July 2014
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.