Communications in Mathematical Sciences

Volume 16 (2018)

Number 6

Interaction of the elementary waves of isentropic flow in a variable cross-section duct

Pages: 1659 – 1684

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n6.a8

Authors

Wancheng Sheng (Department of Mathematics, Shanghai University, Shanghai, China)

Qinglong Zhang (Department of Mathematics, Shanghai University, Shanghai, China)

Abstract

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.

Keywords

duct flow, nonconservative, interaction of elementary waves, Riemann problem

2010 Mathematics Subject Classification

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

Full Text (PDF format)

This work was supported by NSFC 11371240 and 11771274.

Received 12 February 2018

Accepted 8 June 2018

Published 7 February 2019