Open Access
Volume 56, Number 5, September-October 2022
Page(s) 1715 - 1739
Published online 20 July 2022
  1. B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini, One-dimensional conservation laws with nonlocal point constraints on the flux, In Vol. 1 of Crowd Dynamics. Modelling and Simulation in Science, Engineering and Technology, Birkhäuser, Springer, Cham (2018) 103–135. [Google Scholar]
  2. P. Baiti and H.K. Jenssen, Blowup in L for a class of genuinely nonlinear hyperbolic systems of conservation laws. Discrete Contin. Dyn. Syst. 7 (2001) 837–853. [CrossRef] [Google Scholar]
  3. M.K. Banda and M. Herty, Towards a space mapping approach to dynamic compressor optimization of gas networks. Optim. Control Appl. Methods 32 (2011) 253–269. [CrossRef] [Google Scholar]
  4. M.K. Banda, M. Herty and A. Klar, Coupling conditions for gas networks governed by the isothermal Euler equations. Netw. Heterog. Media 1 (2006) 295–314. [CrossRef] [MathSciNet] [Google Scholar]
  5. M.K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks. Netw. Heterog. Media 1 (2006) 41–56. [CrossRef] [MathSciNet] [Google Scholar]
  6. B. Boutin, F. Coquel and P.G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure. Netw. Heterog. Media 16 (2021) 283–315. [CrossRef] [MathSciNet] [Google Scholar]
  7. A. Bressan, Hyperbolic Systems of Conservation Laws, Vol. 20, Oxford University Press, Oxford (2000). [Google Scholar]
  8. A. Bressan, G. Chen, Q. Zhang and S. Zhu, No BV bounds for approximate solutions to p-system with general pressure law. J. Hyperbolic Differ. Equ. 12 (2015) 799–816. [CrossRef] [MathSciNet] [Google Scholar]
  9. A.J. Chorin, Random choice solution of hyperbolic systems. J. Comput. Phys. 22 (1976) 517–533. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Colella, Glimm’s method for gas dynamics. SIAM J. Sci. Statist. Comput. 3 (1982) 76–110. [CrossRef] [MathSciNet] [Google Scholar]
  11. R.M. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint. J. Differ. Equ. 234 (2007) 654–675. [Google Scholar]
  12. A. Corli and M.D. Rosini, Coherence and chattering of a one-way valve. ZAMM Z. Angew. Math. Mech. 99 (2019) 25. [Google Scholar]
  13. A. Corli and M.D. Rosini, Coherence of coupling Riemann solvers for gas flows through flux-maximizing valves. SIAM J. Appl. Math. 79 (2019) 2593–2614. [Google Scholar]
  14. A. Corli, M. Figiel, A. Futa and M.D. Rosini, Coupling conditions for isothermal gas flow and applications to valves. Nonlinear Anal. Real World Appl. 40 (2018) 403–427. [CrossRef] [MathSciNet] [Google Scholar]
  15. C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 4th edition. Springer-Verlag, Berlin (2016). [CrossRef] [Google Scholar]
  16. M. Garavello and B. Piccoli, Traffic Flow on Networks. American Institute of Mathematical Sciences (AIMS), Springfield, MO (2006). [Google Scholar]
  17. M. Garavello and P. Goatin, The Aw-Rascle traffic model with locally constrained flow. J. Math. Anal. Appl. 378 (2011) 634–648. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965) 697–715. [CrossRef] [MathSciNet] [Google Scholar]
  19. E. Godlewski and P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I. The scalar case. Numer. Math. 97 (2004) 81–130. [Google Scholar]
  20. M. Gugat and M. Herty, Existence of classical solutions and feedback stabilization for the flow in gas networks. ESAIM Control Optim. Calc. Var. 17 (2011) 28–51. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  21. M. Gugat and M. Herty, Modeling, control and numerics of gas networks (2020). [Google Scholar]
  22. M. Gugat, M. Herty and V. Schleper, Flow control in gas networks: exact controllability to a given demand. Math. Methods Appl. Sci. 34 (2011) 745–757. [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Gugat, M. Herty and S. Müller, Coupling conditions for the transition from supersonic to subsonic fluid states. Netw. Heterog. Media 12 (2017) 371–380. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Gugat, G. Leugering, A. Martin, M. Schmidt, M. Sirvent and D. Wintergerst, MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Comput. Optim. Appl. 70 (2018) 267–294. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Gugat, G. Leugering, A. Martin, M. Schmidt, M. Sirvent and D. Wintergerst, Towards simulation based mixed-integer optimization with differential equations. Networks 72 (2018) 60–83. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Herty, Modeling, simulation and optimization of gas networks with compressors. Netw. Heterog. Media 2 (2007) 81–97. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Herty and V. Sachers, Adjoint calculus for optimization of gas networks. Netw. Heterog. Media 2 (2007) 733–750. [CrossRef] [MathSciNet] [Google Scholar]
  28. C. Hös and A.R. Champneys, Grazing bifurcations and chatter in a pressure relief valve model. Phys. D 241 (2012) 2068–2076. [CrossRef] [MathSciNet] [Google Scholar]
  29. H. Holden and N.H. Risebro, A mathematical model of traffic flow on a network of unidirectional roads. SIAM J. Math. Anal. 26 (1995) 999–1017. [Google Scholar]
  30. H.K. Jenssen, Blowup for systems of conservation laws. SIAM J. Math. Anal. 31 (2000) 894–908. [CrossRef] [MathSciNet] [Google Scholar]
  31. R.J. LeVeque, Numerical Methods for Conservation Laws. Birkhäuser Verlag, Basel (1990). [CrossRef] [Google Scholar]
  32. A. Martin, M. Möller and S. Moritz, Mixed integer models for the stationary case of gas network optimization. Math. Program. 105 (2006) 563–582. [CrossRef] [MathSciNet] [Google Scholar]
  33. D. Modesti and S. Pirozzoli, Direct numerical simulation of supersonic pipe flow at moderate Reynolds number. Int. J. Heat Fluid Flow 76 (2019) 100–112. [CrossRef] [Google Scholar]
  34. J.D. Taylor, Numerical analysis of fast and slow transients in gas transmission networks. Ph.D. thesis, Heriot-Watt University (1997). [Google Scholar]
  35. E.F. Toro, Riemann solvers and numerical methods for fluid dynamics. Springer-Verlag, Berlin (1997) A practical introduction. [CrossRef] [Google Scholar]
  36. B. Ulanicki and P. Skworcow, Why PRVs tends to oscillate at low flows. Procedia Eng. 89 (2014) 378–385. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you