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

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/q 0 ), 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/q 0 ) 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. MATHEMATICS SUBJECT CLASSIFICATION (MSC): 76M55; 76L05; 76W05 ª 2015 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.

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]…”

Self-Similar Motion of Strong Converging Cylindrical and Spherical Shock Waves in Non-Ideal Stellar Medium

“…The equation of state under equilibrium condition is of Mie-Grüneisen type (Ramu and Ranga Rao 1993;Ramu et al 2014;Narsimhulu et al 2016…”

“…The jump conditions across a shock wave propagating in an electrically conducting and radiating gas are given by (Ramu et al 2014;Narsimhulu et al 2016)…”

Similarity Solution of Spherical Shock Waves -Effect of Viscosity

“…The viscosity term suggested by is included into the hydrodynamic equations for spherically symmetric flow in magnetogasdynamics regime, can be written in Eulerian form [8,14,20,25,26,27] where r and t are independent space and time coordinates ρ, u, p, q and e are density, velocity, pressure, artificial viscosity and internal energy per unit mass respectively and h = µH 2 2 is the magnetic pressure, H and µ being magnetic field strength and the magnetic permeability respectively. The shock position is given by R s (t) and its velocity D = dR s (t)…”