Error Analysis and Model Adaptivity for Flows in Gas Networks

[1] Bundesministerium für Wirtschaft und Energie. Primärenergieverbrauch nach Energieträgern. http://www:bmwi:de. Accessed: 2016-04-19.Search in Google Scholar

[2] M.A. Adewumi and J. Zhou. Simulation of transient flow in natural gas pipelines. 27th Annual Meeting of PSIG (Pipeline Simulation Interest Group), Albuquerque, NM, 1995.Search in Google Scholar

[3] M.K. Banda, M. Herty, and A. Klar. Coupling conditions for gas networks governed by the isothermal Euler equations. Netw. Heterog. Media, 1(2):295-314, 2006.10.3934/nhm.2006.1.295Search in Google Scholar

[4] M.K. Banda, M. Herty, and A. Klar. Gas flow in pipeline networks. Netw. Heterog. Media, 1(1):41-56, March 2006.10.3934/nhm.2006.1.41Search in Google Scholar

[5] K.S. Chapman, P. Krishniswami, V. Wallentine, M. Abbaspour, R. Ranganathan, R. Addanki, J. Sengupta, and L. Chen. Virtual pipeline system testbed to optimize the U.S. natural gas transmission pipeline system. Technical Report DE-FC26-01NT41322, The National Gas Machinery Laboratory, Kansas State University, 2005.Search in Google Scholar

[6] R.M. Colombo and M. Garavello. A well-posed Riemann problem for the p-system at a junction. Netw. and Heterog. Media, 1(3):495-511, 2006.10.3934/nhm.2006.1.495Search in Google Scholar

[7] P. Domschke, O. Kolb, and J. Lang. Adjoint-based error control for the simulation and optimization of gas and water supply networks. Appl. Math. Comput., 259:1003-1018, 2015.10.1016/j.amc.2015.03.029Search in Google Scholar

[8] K. Ehrhardt and M.C. Steinbach. KKT systems in operative planning for gas distribution networks. Proc. Appl. Math. Mech., 4(1):606-607, 2004.10.1002/pamm.200410284Search in Google Scholar

[9] K. Ehrhardt and M.C. Steinbach. Nonlinear optimization in gas networks. In H. G. Bock, E. Kostina, H. X. Phu, and R. Ranacher, editors, Modeling, Simulation and Optimization of Complex Processes, pages 139-148. Springer, Berlin Heidelberg, 2005.10.1007/3-540-27170-8_11Search in Google Scholar

[10] M. Herty, J. Mohring, and V. Sachers. A new model for gas flow in pipe networks. Math. Methods Appl. Sci., 33(7):845-855, 2010.10.1002/mma.1197Search in Google Scholar

[11] S. L. Ke and H. C. Ti. Transient analysis of isothermal gas flow in pipeline networks. Chem. Eng. J., 76(2):169-177, 2000.10.1016/S1385-8947(99)00122-9Search in Google Scholar

[12] A. Martin, M. Möller, and S. Moritz. Mixed integer models for the stationary case of gas network optimization. Math. Program., 105(2):563-582, 2006.10.1007/s10107-005-0665-5Search in Google Scholar

[13] A.J. Osiadacz and M. Chaczykowski. Comparison of isothermal and nonisothermal pipeline gas flow models. Chem. Eng. J., 81(1-3):41-51, 2001.10.1016/S1385-8947(00)00194-7Search in Google Scholar

[14] M. C. Steinbach. On PDE solution in transient optimization of gas networks. J. Comput. Appl. Math., 203(2):345-361, 2007. Special Issue: The first Indo-German Conference on PDE, Scientiffic Computing and Optimization in Applications.10.1016/j.cam.2006.04.018Search in Google Scholar

[15] M.K. Banda and M. Herty. Multiscale modeling for gas flow in pipe networks. Math. Methods Appl. Sci., 31(8):915-936, 2008.10.1002/mma.948Search in Google Scholar

[16] J. Brouwer, I. Gasser, and M. Herty. Gas pipeline models revisited: Model hierarchies, nonisothermal models, and simulations of networks. Multiscale Model. Simul., 9(2):601-623, 2011.10.1137/100813580Search in Google Scholar

[17] P. Domschke. Adjoint-Based Control of Model and Discretization Errors for Gas Transport in Networked Pipelines. PhD thesis, TU Darmstadt, Verlag Dr. Hut, 2011.10.1007/978-3-642-20986-4_1Search in Google Scholar

[18] P. Domschke, O. Kolb, and J. Lang. Adjoint-based control of model and discretisation errors for gas and water supply networks. In X. Yang and S. Koziel, editors, Computational Optimization and Applications in Engineering and Industry, pages 1-17. Springer, Berlin Heidelberg, 2011.10.1007/978-3-642-20986-4_1Search in Google Scholar

[19] N.J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, PA, second edition, 2002.10.1137/1.9780898718027Search in Google Scholar

[20] P. Domschke, O. Kolb, and J. Lang. An adaptive model switching and discretization algorithm for gas flow on networks. Procedia Comput. Sci., 1(1):1331-1340, 2010.10.1016/j.procs.2010.04.148Search in Google Scholar

[21] M. Konstantinov, D.W. Gu, V. Mehrmann, and P. Petkov. Perturbation Theory for Matrix Equations. Studies in Computational Mathematics. Elsevier Science, North Holland, 2003.Search in Google Scholar

[22] R. Le Veque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002.Search in Google Scholar

[23] P. Bales. Hierarchische Modellierung der Eulerschen Flussgleichungen in der Gasdynamik. Diplomarbeit, TU Darmstadt, 2005.Search in Google Scholar

[24] M. Schmidt, M.C. Steinbach, and B.M. Willert. High detail stationary optimization models for gas networks. Optimization and Engineering, 16(1):131-164, 2015.10.1007/s11081-014-9246-xSearch in Google Scholar

[25] International Organization for Standardization. ISO 6976:1995 Natural gas - Calculation of calorific values, density, relative density and Wobbe index from composition. https://www:iso:org/obp/ui/#iso:std:iso: 6976:ed-2:v2:en, 1995. Accessed: 2016-04-20.Search in Google Scholar

[26] A.J. Osiadacz. Simulation and analysis of gas networks. E. & F.N. Spon, London, 1987.Search in Google Scholar

[27] A.J. Osiadacz. Different transient flow models - limitations, advantages, and disadvantages. 28th Annual Meeting of PSIG (Pipeline Simulation Interest Group), San Francisco, CA, 1996.Search in Google Scholar

[28] B. Geiÿler, A. Martin, A. Morsi, and L. Schewe. Using piecewise linear functions for solving MINLPs. In J. Lee and S. Leyffer, editors, Mixed Integer Nonlinear Programming, volume 154 of The IMA Volumes in Mathematics and its Applications, pages 287-314. Springer, New York, 2012.10.1007/978-1-4614-1927-3_10Search in Google Scholar

[29] T. Koch, B. Hiller, M.E. Pfetsch, and L. Schewe. Evaluating Gas Network Capacities. MOS-SIAM Series on Optimization. SIAM, Philadelphia, PA, 2015.10.1137/1.9781611973693Search in Google Scholar

[30] M. Bollhöfer and V. Mehrmann. Numerische Mathematik - Eine projektorientierte Einführung für Ingenieure, Mathematiker und Naturwissenschaftler. vieweg studium; Grundkurs Mathematik. Vieweg+Teubner Verlag, Wiesbaden, 2004.Search in Google Scholar

[31] J.R. Rice. Numerical Methods, Software, and Analysis. Academic Press, San Diego, CA, second edition, 1993.Search in Google Scholar

[32] J.H. Wilkinson. Rounding Errors in Algebraic Processes. Dover books on advanced mathematics. Dover Publications, New York, NY, 1994.Search in Google Scholar

[33] P. Deuffhard and A. Hohmann. Numerical analysis, A first course in scientific computation. De Gruyter Textbook. Walter de Gruyter & Co., Berlin, 1995.10.1515/9783110891997Search in Google Scholar

[34] H. Woźniakowski. Numerical stability for solving nonlinear equations. Numer. Math., 27(4):373-390, 1976.10.1007/BF01399601Search in Google Scholar

[35] G. Strang. Linear Algebra and its Applications. Academic Press, New York, NY, second edition, 1980.Search in Google Scholar

[36] F. Chaitin-Chatelin and V. Frayssé. Lectures on Finite Precision Computations. Software, Environments and Tools. SIAM, Philadelphia, PA, 1996.10.1137/1.9780898719673Search in Google Scholar

[37] M. Padulo, M. S. Campobasso, and M. D. Guenov. Novel Uncertainty Propagation Method for Robust Aerodynamic Design. AIAA Journal, 49(3):530-543, 2011.10.2514/1.J050448Search in Google Scholar

[38] S. Moritz. A Mixed Integer Approach for the Transient Case of Gas Network Optimization. PhD thesis, TU Darmstadt, 2006.Search in Google Scholar

[39] C.T. Kelley. Iterative Methods for Linear and Nonlinear Equations. Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, 1995.10.1137/1.9781611970944Search in Google Scholar

[40] O. Kolb, J. Lang, and P. Bales. An implicit box scheme for subsonic compressible flow with dissipative source term. Numer. Algorithms, 53(2- 3):293-307, 2010.10.1007/s11075-009-9287-ySearch in Google Scholar

[41] T. J. Ypma. The effect of rounding errors on Newton-like methods. IMA J. Numer. Anal., 3(1):109-118, 1983.10.1093/imanum/3.1.109Search in Google Scholar

[42] C. Grossmann and H. Roos. Numerical treatment of partial differential equations. Universitext. Springer, Berlin, 2007. Translated and revised from the 3rd (2005) German edition by Martin Stynes.10.1007/978-3-540-71584-9Search in Google Scholar

[43] V. Mehrmann and J.J. Stolwijk. Error analysis for the Euler equations in purely algebraic form. Technical Report 2015/06, TU Berlin, Institut für Mathematik, 2015.Search in Google Scholar