Efficient numerical methods for gas network modeling and simulation

Yue Qiu; Sara Grundel; Martin Stoll; Peter Benner; Yue Qiu; Sara Grundel; Martin Stoll; Peter Benner

doi:10.3934/nhm.2020018

Networks and Heterogeneous Media

2020, Volume 15, Issue 4: 653-679. doi: 10.3934/nhm.2020018

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Efficient numerical methods for gas network modeling and simulation

Yue Qiu ^{1,2
,
,},
Sara Grundel ^{2
,},
Martin Stoll ^{3
,},
Peter Benner ^{2
,}

1.
School of Information Science and Technology, ShanghaiTech University, 393 Middle Huaxia Road, 201210, Shanghai, China
2.
Computational Methods for Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106, Magdeburg, Germany
3.
Faculty of Mathematics, Technische Universität Chemnitz, Reichenhainer Straße 41, 09126, Chemnitz, Germany

Received: 01 August 2019 Revised: 01 August 2020 Published: 26 August 2020
Primary: 65F08, 37M05, 37N30, 94C15

We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a system of nonlinear differential algebraic equations (DAEs). With our modeling approach, we reduce the number of algebraic constraints, which correspond to the $ (2,2) $ block in our semi-explicit DAE model, to the order of junction nodes in the network, where a junction node couples at least three pipelines. We can furthermore ensure that the $ (1, 1) $ block of all system matrices including the Jacobian is block lower triangular by using a specific ordering of the pipes of the network. We then exploit this structure to propose an efficient preconditioner for the fast simulation of the network. We test our numerical methods on benchmark problems of (well-)known gas networks and the numerical results show the efficiency of our methods.
- Gas networks modeling,
- isothermal Euler equation,
- directed acyclic graph (DAG),
- differential algebraic equation (DAE),
- preconditioning
Citation: Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner. Efficient numerical methods for gas network modeling and simulation[J]. Networks and Heterogeneous Media, 2020, 15(4): 653-679. doi: 10.3934/nhm.2020018

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Abstract

We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a system of nonlinear differential algebraic equations (DAEs). With our modeling approach, we reduce the number of algebraic constraints, which correspond to the $ (2,2) $ block in our semi-explicit DAE model, to the order of junction nodes in the network, where a junction node couples at least three pipelines. We can furthermore ensure that the $ (1, 1) $ block of all system matrices including the Jacobian is block lower triangular by using a specific ordering of the pipes of the network. We then exploit this structure to propose an efficient preconditioner for the fast simulation of the network. We test our numerical methods on benchmark problems of (well-)known gas networks and the numerical results show the efficiency of our methods.

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