  We are concerned with the large time behavior of solutions to the Cauchy
problem of the one-dimensional compressible micropolar fluid model without
viscosity, where the far-field states of the initial data are prescribed to be
different. If the corresponding Riemann problem of the compressible Euler
system admits a contact discontinuity and two rarefaction waves solutions, we
show that for such a non-viscous model, the combination of the viscous contact
wave with two rarefaction waves is time-asymptotically stable provided that the
strength of the composite wave and the initial perturbation are sufficiently
small. The proof is given by an elementary $L^2$ energy method.
