Vanishing magnetic field limits of solutions to the non-isentropic Chaplygin gas magnetogasdynamics equations

This paper studied the Riemann problem for the non-isentropic Chaplygin gas magnetogasdynamics equations and investigated the general asymptotic behavior of its Riemann solutions. Due to the influence of the source term in the equations, the Riemann solutions for the non-isentropic Chaplygin gas magnetogasdynamics equations are no longer self-similar. We performed the analysis after eliminating the source term by using a velocity transformation. When the Riemann initial data of density and velocity satisfied the condition $v_{–}\frac{1}{{\rho }_{-}}\ge v_{+}+\frac{1}{{\rho }_{+}}$, as the reciprocal of magnetic flux density $\mu$ tended to zero, the Riemann solutions of the non-isentropic Chaplygin gas magnetogasdynamics equations converged to the delta shock solutions of the non-isentropic Chaplygin Euler equations. Otherwise, the Riemann solutions converged to a contact discontinuity of the non-isentropic Chaplygin Euler equations.