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The interaction of elementary waves for nonisentropic flow in a variable cross-section duct

The interaction of elementary waves for isentropic flow in a variable cross-section duct is obtained (\cite{ShengZhang}). The authors have discussed rarefaction wave or shock wave interacts with stationary wave. In this paper, we extend their results to the nonisentropic flow. It can be proved that if one changes $(u,ρ)$ plane in isentropic flow with $(u,p)$ plane in nonisentropic case, the interaction results of rarefaction wave or shock wave with stationary wave can be moved parallel from the isentropic case when contact discontinuity is involved. Thus we mainly focus on the interactions between contact discontinuity and stationary wave. Some numerical results are given to verify our analysis. The results can apply to the interaction of more complicated wave patterns.