Vanishing flux perturbation, pressure, and magnetic field limit in a Chaplygin magnetogasdynamics

Abstract

The Riemann problem for a Chaplygin magnetogasdynamics system of compressible fluid flow with a triple parameter perturbation containing flux, pressure, and magnetic field is first solved. Second, it is shown that as the triple parameter flux perturbation, pressure, and magnetic field vanish, any Riemann solution containing two shock waves tends to a delta-shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to a vacuum solution to the transport equations. Third, it is also proved that as the double parameter flux perturbation and magnetic field vanish, any Riemann solution containing two shock waves approaches a delta-shock solution to the Chaplygin gas equations and any Riemann solution containing two rarefaction waves tends to a solution containing two contact discontinuities of the Chaplygin gas equations. Finally, some numerical results are presented to be consistent with the theoretical analysis.