TY - JOUR A1 - Domschke, Pia A1 - Kolb, Oliver A1 - Lang, Jens T1 - Fast and Reliable Transient Simulation and Continuous Optimization of Large-Scale Gas Networks N2 - We are concerned with the simulation and optimization of large-scale gas pipeline systems in an error-controlled environment. The gas flow dynamics is locally approximated by sufficiently accurate physical models taken from a hierarchy of decreasing complexity and varying over time. Feasible work regions of compressor stations consisting of several turbo compressors are included by semiconvex approximations of aggregated characteristic fields. A discrete adjoint approach within a first-discretize-then-optimize strategy is proposed and a sequential quadratic programming with an active set strategy is applied to solve the nonlinear constrained optimization problems resulting from a validation of nominations. The method proposed here accelerates the computation of near-term forecasts of sudden changes in the gas management and allows for an economic control of intra-day gas flow schedules in large networks. Case studies for real gas pipeline systems show the remarkable performance of the new method. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1007/s00186-021-00765-7 PB - Mathematical Methods of Operations Research ER - TY - INPR A1 - Domschke, Pia A1 - Hiller, Benjamin A1 - Lang, Jens A1 - Mehrmann, Volker A1 - Morandin, Riccardo A1 - Tischendorf, Caren T1 - Gas Network Modeling: An Overview N2 - With this overview we want to provide a compilation of different models for the description of gas flow in networks in order to facilitate the introduction to the topic. Special attention is paid to the hierarchical structure inherent to the modeling, and the detailed description of individual components such as valves and compressors. Also included are network model classes based on purely algebraic relations, and energy-based port-Hamiltonian models. A short overview of basic numerical methods and concepts for the treatment of hyperbolic balance equations is also given. We do not claim completeness and refer in many places to the existing literature. The idea of a model catalog came to us in the context of the application for the CRC/Transregio 154 ``Mathematical modeling, simulation and optimization using the example of gas networks''. The present English translation is an extension from [P. Domschke, B. Hiller, J. Lang, and C. Tischendorf. Modellierung von Gasnetzwerken: Eine Übersicht. Preprint, TRR 154, 2017]. At this point we would like to thank the DFG for its support. Y1 - 2021 ER - TY - INPR A1 - Domschke, Pia A1 - Hiller, Benjamin A1 - Lang, Jens A1 - Tischendorf, Caren T1 - Modellierung von Gasnetzwerken: Eine Übersicht N2 - Mit dieser Übersicht wollen wir eine Zusammenstellung von unterschiedlichen Modellen zur Beschreibung des Gasflusses in Netzwerken bereitstellen, um den Einstieg in das Thema zu erleichtern. Besonderes Augenmerk wird dabei auf die der Modellierung inneliegende hierarchische Struktur und die detaillierte Beschreibung einzelner Bauteile wie Ventile und Kompressoren gelegt. Daneben finden sich ebenfalls Netzmodellklassen, die auf rein algebraische Relationen aufbauen. Am Ende geben wir einen kurzen Überblick über grundlegende numerische Verfahren und Konzepte zur Behandlung von hyperbolischen Bilanzgleichungen. Wir erheben keinen Anspruch auf Vollständigkeit und verweisen an vielen Stellen auf die bestehende Literatur. Die Idee eines Modellkataloges ist uns im Rahmen der Antragstellung zum SFB/Transregio 154 „Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken“ gekommen. Wir möchten an dieser Stelle die Förderung durch die DFG dankend erwähnen. KW - Euler-Gleichungen, isotherme Euler-Gleichungen, Modellhierarchie, Netzelemente Y1 - 2017 VL - 2717 ER - TY - JOUR A1 - Domschke, Pia A1 - Groß, Martin A1 - Hiller, Benjamin A1 - Hante, Falk A1 - Schewe, Lars A1 - Schmidt, Martin T1 - Mathematische Modellierung, Simulation und Optimierung von Gastransportnetzwerken JF - gwf-gas/erdgas Y1 - 2015 VL - 11 SP - 880 EP - 885 ER - TY - JOUR A1 - Domschke, Pia A1 - Dua, Aseem A1 - Stolwijk, Jeroen J. A1 - Lang, Jens A1 - Mehrmann, Volker T1 - Adaptive Refinement Strategies for the Simulation of Gas Flow in Networks using a Model Hierarchy N2 - A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing the simulation error below a prescribed tolerance while keeping the computational costs low. While spatial and temporal stepsize adaptivity is well studied in the literature, model adaptivity is a new field of research. The problem of finding an optimal refinement strategy that combines these three types of adaptivity is a generalisation of the unbounded knapsack problem. A refinement strategy that is currently used in gas flow simulation software is compared to two novel greedy-like strategies. Both a theoretical experiment and a realistic gas flow simulation show that the novel strategies significantly outperform the current refinement strategy with respect to the computational cost incurred. KW - gas supply networks KW - model hierarchy KW - error estimators KW - model adaptivity KW - refinement strategies Y1 - 2017 U6 - https://doi.org/10.1553/etna_vol48s97 VL - Electronic Transactions on Numerical Analysis IS - Vol. 48 SP - 97 EP - 113 ER - TY - JOUR A1 - Mindt, Pascal A1 - Lang, Jens A1 - Domschke, Pia T1 - Entropy-Preserving Coupling of Hierarchical Gas Models N2 - This paper is concerned with coupling conditions at junctions for transport models which differ in their fidelity to describe transient flow in gas pipelines. It also includes the integration of compressors between two pipes with possibly different models. A hierarchy of three one-dimensional gas transport models is built through the 3 × 3 polytropic Euler equations, the 2 × 2 isentropic Euler equations and a simplified version of it for small velocities. To ensure entropy preservation, we make use of the novel entropy-preserving coupling conditions recently proposed by Lang and Mindt [Netw. Heterog. Media, 13:177-190, 2018] and require the equality of the total enthalpy at the junction and that the specific entropy for pipes with outgoing flow equals the convex combination of all entropies that belong to pipes with incoming flow. We prove the existence and uniqueness of solutions to generalised Riemann problems at a junction in the neighbourhood of constant coupling functions and stationary states which belong to the subsonic region. This provides the basis for the well-posedness of certain Cauchy problems for initial data with sufficiently small total variation. Y1 - 2018 U6 - https://doi.org/doi:10.1137/19M1240034 VL - SIAM Journal on Mathematical Analysis IS - 51 SP - 4754 EP - 4775 ER - TY - INPR A1 - Domschke, Pia A1 - Giesselmann, Jan A1 - Lang, Jens A1 - Breiten, Tobias A1 - Mehrmann, Volker A1 - Morandin, Riccardo A1 - Hiller, Benjamin A1 - Tischendorf, Caren T1 - Gas Network Modeling: An Overview (Extended English Version) N2 - With this overview we want to provide a compilation of different models for the description of gas flow in networks in order to facilitate the introduction to the topic. Special attention is paid to the hierarchical structure inherent to the modeling, and the detailed description of individual components such as valves and compressors. Also included are network model classes based on purely algebraic relations, and energy-based port-Hamiltonian models. A short overview of basic numerical methods and concepts for the treatment of hyperbolic balance equations is also given. We do not claim completeness and refer in many places to the existing literature. Y1 - 2023 ER - TY - JOUR A1 - Lang, Jens A1 - Domschke, Pia A1 - Strauch, Elisa T1 - Adaptive Single- and Multilevel Stochastic Collocation Methods for Uncertain Gas Transport in Large-Scale Networks N2 - In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is modelled by a hierarchy of hyperbolic systems of balance laws based on the isentropic Euler equations. We extend a novel adaptive strategy for solving elliptic PDEs with random data, recently proposed and analysed by Lang, Scheichl, and Silvester [J. Comput. Phys., 419:109692, 2020], to uncertain gas transport problems. Sample-dependent adaptive meshes and a model refinement in the physical space is combined with adaptive anisotropic sparse Smolyak grids in the stochastic space. A single-level approach which balances the discretization errors of the physical and stochastic approximations and a multilevel approach which additionally minimizes the computational costs are considered. Two examples taken from a public gas library demonstrate the reliability of the error control of expectations calculated from random quantities of interest, and the further use of stochastic interpolants to, e.g., approximate probability density functions of minimum and maximum pressure values at the exits of the network. Y1 - 2021 VL - In: Mesh Generation and Adaptation, Cutting-Edge Techniques. R. Sevilla, S. Perotto, K. Morgan (eds.), SEMA-SIMAI Springer Series IS - Vol. 30 SP - 113 EP - 135 ER -