The composite wave in the Riemann solutions for macroscopic production model

Abstract

In this paper, the Riemann solutions for the macroscopic production model with chaplygin gas under some special initial data are constructively obtained in the fully explicit form. An interesting composite wave RδJ is observed, it is formed by a rarefaction wave R and a left-contact delta discontinuity δJ attached to the wavefront of the rarefaction wave. Furthermore, this delta discontinuity gradually absorbs the rarefaction wave and eventually forms a delta shock wave under some suitable initial condition. In addition, we give some typical numerical results that coincide well with the theoretical analysis.