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Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 215--225 | DOI:10.5890/DNC.2025.03.013

Ravilisetty Revathi$^{1}$, Addepalli Ramu$^{2}$

$^1$ School of Sciences, Woxsen University, Telangana, India, 502345

$^2$ Department of Mathematics, BITS - Pilani, Hyderabad, Telangana, India, 500078

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Abstract

A similarity solution for cylindrically converging shock waves of symmetric flow in MHD propagating into a medium, plasma governed by the equation of state (EOS) of Mie-Gr$\ddot{u}$neisen type, is calculated. The governing equations of flow with total energy and constant specific heats are considered in the Eulerian form. These equations are reduced to a system of differential equations of Poincare type using similarity transformations. The transformed system is then reduced to a finite difference system of equations and solved numerically using MATLAB. In the present work, different non-ideal EOS of Mie-Gr$\ddot{u}$neisen type are considered with suitable material constants. Similarity exponent $\alpha$, which varies with the measure of shock strength, $\beta$ for the considered EOS are evaluated. It is observed that the measure of shock strength $\beta$ affects the shock front. Further, the effect of non-idealness parameters, magnetic field strength on the flow variables are presented.

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