Vanishing pressure and magnetic field limit of solutions to the nonisentropic magnetogasdynamics

Abstract

The Riemann problem of the nonisentropic magnetogasdynamics is analytically solved. Then it is proved that, as the pressure and transverse magnetic field both vanish, any Riemann solution containing two shocks and a possibly one-contact-discontinuity to the nonisentropic magnetogasdynamics tends to a delta shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted δ-measure which forms the delta shock wave; any Riemann solution containing two rarefaction waves and a possibly one-contact-discontinuity to the nonisentropic magnetogasdynamics tends to a two-contact-discontinuity solution to the transport equations, and the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. Some numerical simulations are also presented to confirm the theory analysis.