An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium. It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave. Also, an analytical expression for the total energy in a non-ideal medium is derived.
This paper investigates the problem of propagation of planar and non-planar weak shock waves in a non-ideal medium. The mathematical formulation developed in this work leads to a closed system of coupled transport equations which efficiently describes the strength of a shock wave and the first order discontinuities induced behind it. The influence of the parameter of non-idealness and the non planar configuration of the wavefront on the nonlinear distortion, attenuation and shock formation of pulses, are discussed in detail. An analytical expression for the shock formation distance is obtained and a direct comparison between the ideal versus the non ideal gas flow is established. Also, the usual asymptotic decay laws for weak shock are recovered.
This article aims at studying one dimensional unsteady planar and cylindrically symmetric flow involving shocks under the influence of magnetic field. The method of generalized wavefront expansion (GWE) is employed to derive a coupled system of nonlinear transport equations for the jump of field variables and of its spatial derivatives across the shock, which, in turn determine the evolution of wave amplitude and admit a solution that agrees with the classical decay laws of weak shocks. A closed form solution exhibiting the features of nonlinear steepening of the wave front. A general criterion for a compression wave to steepen into a shock is derived. An analytic expression elucidating how the shock formation distance is influenced by the magnetic field strength is obtained. Also, the effects of geometrical spreading and nonlinear convection on the distortion of the waveform are investigated in the presence of magnetic field
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