Communications in Mathematical Sciences
Volume 16 (2018)
Interaction of the elementary waves of isentropic flow in a variable cross-section duct
Pages: 1659 – 1684
The equations of fluid in a variable cross-section duct are nonconservative because of the source term. Recently, the Riemann solutions of the equations for the compressible duct flow have been obtained. The authors also obtained the elementary waves including rarefaction waves, shock waves and stationary wave. In this paper, we mainly discuss the interactions of rarefaction wave and shock wave with the stationary wave, for the cases in which the cross-section area is either decreasing or increasing. The large-time behavior is shown in each case.
duct flow, nonconservative, interaction of elementary waves, Riemann problem
2010 Mathematics Subject Classification
35L50, 35L60, 35L65, 35L80, 35R35
This work was supported by NSFC 11371240 and 11771274.
Received 12 February 2018
Accepted 8 June 2018
Published 7 February 2019