Riemann problem and wave interactions in Magnetogasdynamics

Abstract

a b s t r a c tThis paper is mainly concerned with the Riemann problem for one-dimensional ideal isentropic Magnetogasdynamics with transverse magnetic field. The existence and uniqueness of the solutions of the Riemann problem are obtained constructively with the characteristic method. Furthermore, we investigate the interactions of the elementary waves.

Solution of the Riemann Problem in magnetogasdynamics

“…It may be noted here that the velocity profiles corresponding to characteristic curves for 1-shock is convex whereas for 3-shock is concave in nature which is also evident from the analytical solutions obtained. It has also been observed that an increase in the parameters ε 1 and ε 2 have reverse effect on the velocity profiles whereas both the parameters have similar effect on the density profiles which also agrees with the earlier results obtained by another method (Liu and Sun [21]). …”

The Riemann problem and the limit solutions as magnetic field vanishes to magnetogasdynamics for generalized Chaplygin gas

“…Since the full governing system for magnetogasdynamics is highly nonlinear and more complicated, it is necessary to study the various simplified models. One of the simplified model is the assumption that the flow wherein magnetic and velocity fields are orthogonal everywhere, such as in [5,10,11,12]. In the present paper, we consider the system of equations which governs the one dimensional unsteady simple flow of an isentropic, inviscid and perfectly conducting compressible fluid, subject to a transverse magnetic field, can be written as the following conservation laws    ρ t + (ρu) x = 0,…”

Lie group analysis and propagation of weak discontinuity in one-dimensional ideal isentropic magnetogasdynamics

“…We consider the PDEs, governing the one dimensional unsteady flow of an ideal isentropic, inviscid and perfectly conducting compressible fluid, subjected to a transverse magnetic field as follows [20]:…”