Numerical study of shock waves in non-ideal magnetogasdynamics (MHD)

Authors

Department of Mathematics, BITS-Pilani, Hyderabad Campus, India

10.21608/joems.2016.386822

Abstract

One-dimensional unsteady adiabatic flow of strong converging shock waves in cylindrical
or spherical symmetry in MHD, which is propagating into plasma, is analyzed. The plasma is
assumed to be non-ideal gas whose equation of state is of Mie–Gruneisen type. Suitable transformations
reduce the governing equations into ordinary differential equations of Poincare type. In the
present work, McQueen and Royce equations of state (EOS) have been considered with suitable
material constants and the spherical and cylindrical cases are worked out in detail to investigate
the behavior and the influence on the shock wave propagation by energy input and b(q/q0), the
measure of shock strength. The similarity solution is valid for adiabatic flow as long as the counter
pressure is neglected. The numerical technique applied in this paper provides a global solution to
the implosion problem for the flow variables, the similarity exponent a for different Gruneisen
parameters. It is shown that increasing b(q/q0) does not automatically decelerate the shock front
but the velocity and pressure behind the shock front increases quickly in the presence of the magnetic
field and decreases slowly and become constant. This becomes true whether the piston is accelerated,
is moving at constant speed or is decelerated. These results are presented through the
illustrative graphs and tables. The magnetic field effects on the flow variables through a medium
and total energy under the influence of strong magnetic field are also presented.

Keywords

Journal of the Egyptian Mathematical Society
Volume 24, Issue 1
2016
Pages 116-124

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