Modeling, simulation and optimization of gas networks with compressors

Previous Article
Gaussian estimates for a heat equation on a network
NHM Home
This Issue
Next Article
Derivation and analysis of a fluid-dynamical model in thin and long elastic vessels

March 2007, 2(1): 81-97. doi: 10.3934/nhm.2007.2.81

Modeling, simulation and optimization of gas networks with compressors

1.	Department of Mathematics, Universität Kaiserslautern, AG Technomathematik, P.O. Box 3049, D-67663 Kaiserslautern, Germany

Received July 2006 Revised October 2006 Published December 2006

Abstract
Related Papers

We consider gas flow in pipeline networks governed by the isothermal Euler equations and introduce a new modeling of compressors in gas networks. Compressor units are modeled as pipe–to–pipe intersections with additional algebraic coupling conditions for the compressor behavior. We prove existence and uniqueness of solutions with respect to these conditions and use the results for numerical simulation and optimization of gas networks.

Keywords: Gas networks, Isothermal Euler equations, optimization.

Mathematics Subject Classification: Primary: 76N15; Secondary: 35Lx.

Citation: Michael Herty. Modeling, simulation and optimization of gas networks with compressors. Networks & Heterogeneous Media, 2007, 2 (1) : 81-97. doi: 10.3934/nhm.2007.2.81

[1]	Mapundi K. Banda, Michael Herty, Axel Klar. Coupling conditions for gas networks governed by the isothermal Euler equations. Networks & Heterogeneous Media, 2006, 1 (2) : 295-314. doi: 10.3934/nhm.2006.1.295
[2]	Michael Herty, Veronika Sachers. Adjoint calculus for optimization of gas networks. Networks & Heterogeneous Media, 2007, 2 (4) : 733-750. doi: 10.3934/nhm.2007.2.733
[3]	Ju Ge, Wancheng Sheng. The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2733-2748. doi: 10.3934/cpaa.2014.13.2733
[4]	Martin Gugat, Markus Dick. Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Mathematical Control & Related Fields, 2011, 1 (4) : 469-491. doi: 10.3934/mcrf.2011.1.469
[5]	Manwai Yuen. Cylindrical blowup solutions to the isothermal Euler-Poisson equations. Conference Publications, 2011, 2011 (Special) : 1448-1456. doi: 10.3934/proc.2011.2011.1448
[6]	Yanbo Hu, Tong Li. The regularity of a degenerate Goursat problem for the 2-D isothermal Euler equations. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3317-3336. doi: 10.3934/cpaa.2019149
[7]	Markus Dick, Martin Gugat, Günter Leugering. A strict $H^1$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 225-244. doi: 10.3934/naco.2011.1.225
[8]	Yulan Xu, Yanping Dou. Large BV solutions to Euler equations in the isothermal self-gravitating gases with damping. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1451-1467. doi: 10.3934/cpaa.2009.8.1451
[9]	Mapundi K. Banda, Michael Herty, Axel Klar. Gas flow in pipeline networks. Networks & Heterogeneous Media, 2006, 1 (1) : 41-56. doi: 10.3934/nhm.2006.1.41
[10]	Martin Gugat, Falk M. Hante, Markus Hirsch-Dick, Günter Leugering. Stationary states in gas networks. Networks & Heterogeneous Media, 2015, 10 (2) : 295-320. doi: 10.3934/nhm.2015.10.295
[11]	Huahui Li, Zhiqiang Shao. Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2373-2400. doi: 10.3934/cpaa.2016041
[12]	Fabian Rüffler, Volker Mehrmann, Falk M. Hante. Optimal model switching for gas flow in pipe networks. Networks & Heterogeneous Media, 2018, 13 (4) : 641-661. doi: 10.3934/nhm.2018029
[13]	Radu C. Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo. Flow optimization in vascular networks. Mathematical Biosciences & Engineering, 2017, 14 (3) : 607-624. doi: 10.3934/mbe.2017035
[14]	Giuseppe Buttazzo, Filippo Santambrogio. Asymptotical compliance optimization for connected networks. Networks & Heterogeneous Media, 2007, 2 (4) : 761-777. doi: 10.3934/nhm.2007.2.761
[15]	Bernard Ducomet, Alexander Zlotnik. On a regularization of the magnetic gas dynamics system of equations. Kinetic & Related Models, 2013, 6 (3) : 533-543. doi: 10.3934/krm.2013.6.533
[16]	Ö. Uğur, G. W. Weber. Optimization and dynamics of gene-environment networks with intervals. Journal of Industrial & Management Optimization, 2007, 3 (2) : 357-379. doi: 10.3934/jimo.2007.3.357
[17]	Okihiro Sawada. Analytic rates of solutions to the Euler equations. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1409-1415. doi: 10.3934/dcdss.2013.6.1409
[18]	Luigi Ambrosio. Variational models for incompressible Euler equations. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 1-10. doi: 10.3934/dcdsb.2009.11.1
[19]	Jianwei Yang, Ruxu Lian, Shu Wang. Incompressible type euler as scaling limit of compressible Euler-Maxwell equations. Communications on Pure & Applied Analysis, 2013, 12 (1) : 503-518. doi: 10.3934/cpaa.2013.12.503
[20]	Yongcai Geng. Singularity formation for relativistic Euler and Euler-Poisson equations with repulsive force. Communications on Pure & Applied Analysis, 2015, 14 (2) : 549-564. doi: 10.3934/cpaa.2015.14.549

2017 Impact Factor: 1.187

American Institute of Mathematical Sciences