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E Isaacson, B Temple (1995)
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The Riemann problem for isentropic van der Waals fluid flows in a nozzle with dis- continuous cross-section is investigated. The pressure, expressed as a function of the density, is increasing and admits two inflection points. The model is not strictly hyper- bolic, and the characteristic fields are not genuinely nonlinear. Since the model is written in Eulerian coordinates, it is hard to directly examine the Liu entropy condi- tion. There may exist up to four stationary jumps from a given state. After imposing the admissibility criterion, two admissible stationary jumps may also co-exist. This leads to the multiple solutions of the Riemann problem for van der Waals fluids. Keywords Shock · Nozzle · van der Waals fluid · Riemann problem · Entropy condition Mathematics Subject Classification 35L40 · 35L65 · 76L05 · 76N10 1 Introduction In this paper, we consider the Riemann problem for the following model of an isen- tropic fluid of van der Waals type flowing in a nozzle with variable cross-section Mai Duc Thanh mdthanh@hcmiu.edu.vn Duong Xuan Vinh xvinhduong@gmail.com Faculty of Applied Science, University of Technology (Vietnam National University-HCM), 268 Ly Thuong Kiet street, District 10, Ho Chi Minh City, Vietnam Department of Mathematics, International University
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Aug 17, 2019
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