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 [W.C. Sheng and Q.L. Zhang, Commun. Math. Sci., 16:1659–1684, 2018]. The authors have discussed rarefaction wave or shock wave interactions with stationary wave. In this paper, we extend their results to the nonisentropic flow. It can be proved that if one changes $(u,\rho)$ 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.

Keywords

duct flow, interaction of elementary waves, non-isentropic, Riemann problem

2010 Mathematics Subject Classification

35L50, 35L60, 35L65, 35L80, 35R35

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This work was sponsored by the K.C. Wong Magna Fund of Ningbo University.

Received 5 November 2019

Accepted 21 December 2020

Published 18 June 2021