Abstract
We are interested in the simulation and optimization of gas and water transport in networks. Those networks consist of pipes and various other components like compressor/pumping stations and valves. The flow through the pipes can be described by different models based on the Euler equations, including hyperbolic systems of partial differential equations. For the other components, algebraic or ordinary differential equations are used. Depending on the data, different models can be used in different regions of the network. We present a strategy that adaptively applies the models and discretizations, using adjoint-based error estimators to maintain the accuracy of the solution. Finally, we give numerical examples for both types of networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abreu, J., Cabrera, E., Izquierdo, J., García-Serra, J.: Flow modeling in pressurized systems revisited. Journal of Hydraulic Engineering 125(11), 1154–1169 (1999)
Bales, P., Kolb, O., Lang, J.: Hierarchical modelling and model adaptivity for gas flow on networks. In: Allen, G., Nabrzyski, J., Seidel, E., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2009. LNCS, vol. 5544, pp. 337–346. Springer, Heidelberg (2009)
Becker, R., Rannacher, R.: An optimal control approach to a posteriori error estimation in finite element methods. Acta numerica 10, 1–102 (2001)
Braack, M., Ern, A.: A posteriori control of modeling errors and discretization errors. SIAM Journal of Multiscale Modeling and Simulation 1(2), 221–238 (2003)
Burgschweiger, J., Gnädig, B., Steinbach, M.C.: Optimization models for operative planning in drinking water networks. Optimization and Engineering 10(1), 43–73 (2009)
Domschke, P., Kolb, O., Lang, J.: An adaptive model switching and discretization algorithm for gas flow on networks. In: Procedia Computer Science ICCS 2010, vol. 1(1), pp. 1325–1334 (2010)
Domschke, P., Kolb, O., Lang, J.: Adjoint-based control of model and discretisation errors for gas flow in networks. Int. J. Mathematical Modelling and Numerical Optimisation 2(2), 175–193 (2011)
Ehrhardt, K., Steinbach, M.C.: Nonlinear optimization in gas networks. In: Bock, H.G., Kostina, E.A., Phu, H.X., Ranacher, R. (eds.) Modeling, Simulation and Optimization of Complex Processes, pp. 139–148. Springer, Heidelberg (2005)
Hähnlein, C.: Numerische Modellierung zur Betriebsoptimierung von Wasserverteilnetzen. PhD thesis, TU Darmstadt (2008)
Herty, M.: Modeling, simulation and optimization of gas networks with compressors. Networks and Heterogeneous Media 2(1), 81–97 (2007)
Kolb, O., Lang, J., Bales, P.: An implicit box scheme for subsonic compressible flow with dissipative source term. Numerical Algorithms 53(2), 293–307 (2010)
Martin, A., Möller, M., Moritz, S.: Mixed integer models for the stationary case of gas network optimization. Mathematical Programming 105, 563–582 (2006)
Moritz, S.: A Mixed Integer Approach for the Transient Case of Gas Network Optimization. PhD thesis, TU Darmstadt (2006)
Rossman, L.A.: EPANET 2 users manual. U.S. Environmental Protection Agency, Cincinnati, OH (2000)
Sekirnjak, E.: Transiente Technische Optimierung (TTO-Prototyp). Technical report, PSI AG (November 2000)
SIMONE Research Group, http://www.simone.eu
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Domschke, P., Kolb, O., Lang, J. (2011). Adjoint-Based Control of Model and Discretization Errors for Gas and Water Supply Networks. In: Yang, XS., Koziel, S. (eds) Computational Optimization and Applications in Engineering and Industry. Studies in Computational Intelligence, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20986-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-20986-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20985-7
Online ISBN: 978-3-642-20986-4
eBook Packages: EngineeringEngineering (R0)