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Riemann Problem for van der Waals Fluids in Nozzle with Cross-Sectional Jump

Riemann Problem for van der Waals Fluids in Nozzle with Cross-Sectional Jump 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Riemann Problem for van der Waals Fluids in Nozzle with Cross-Sectional Jump

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References (30)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-019-00166-9
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Aug 17, 2019

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