Delta shocks and vacuum states in the Riemann solutions of Chaplygin Euler equations as pressure and magnetic field drop to zero

Abstract

The aim of this study is to solve the Riemann problem of isentropic magnetogasdynamics equations for a more realistic version of the extended Chaplygin gas model. The analysis demonstrates that under some special circumstances, delta shock and vacuum appear in the solution, describing the phenomena of concentration and cavitation, respectively. By examining the limiting behavior, it is obtained that solutions coincide with corresponding Riemann solutions of the transport equations when both the magnetic field and pressure drop to zero.