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Exact Riemann solutions to compressible Euler equations in ducts with discontinuous cross-section. (English) Zbl 1263.35178
The authors consider the Euler equations modeling compressible one-dimensional fluid flow through a duct of variable cross-section. The polytropic equation closes the system. The exact Riemann solutions to the system are constructed for arbitrary initial data. The bifurcations leading to non-uniqueness are revealed.

MSC:
35Q31 Euler equations
35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
76H05 Transonic flows
35F25 Initial value problems for nonlinear first-order PDEs
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References:
[1] Andrianov N., SIAM J. Appl. Math. 64 pp 878–
[2] DOI: 10.1016/j.jcp.2003.10.006 · Zbl 1115.76414
[3] Clain S., J. Comput. Phys. 22 pp 8214–
[4] Courant A., Supersonic Flow and Shock Waves (1999) · Zbl 0041.11302
[5] DOI: 10.1016/0022-0396(73)90043-0 · Zbl 0262.35038
[6] Dulov V. G., Vestnik leningrad. Univ. 19 pp 76–
[7] Evans L. C., Partial Differential Equations (1998) · Zbl 0902.35002
[8] DOI: 10.1016/S0045-7930(99)00038-9 · Zbl 0986.76051
[9] DOI: 10.1016/j.anihpc.2004.02.002 · Zbl 1086.35069
[10] DOI: 10.1137/0152073 · Zbl 0794.35100
[11] DOI: 10.4310/CMS.2003.v1.n4.a6 · Zbl 1091.35044
[12] Liu T. P., Arch. Ration. Mech. Anal. 23 pp 1–
[13] DOI: 10.1063/1.527751 · Zbl 0662.35068
[14] DOI: 10.1016/j.jcp.2004.10.023 · Zbl 1203.76117
[15] DOI: 10.1016/0898-1221(86)90173-2 · Zbl 0611.35060
[16] DOI: 10.1016/j.compfluid.2011.09.004 · Zbl 1271.76294
[17] DOI: 10.1007/978-1-4612-0873-0
[18] DOI: 10.1137/080724095 · Zbl 1181.35146
[19] DOI: 10.1007/978-3-662-03490-3
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