Numerical Aspects of Model Order Reduction for Gas Transportation Networks

Grundel, Sara; Hornung, Nils; Roggendorf, Sarah

doi:10.1007/978-3-319-27517-8_1

Cited by 10 publications

(34 citation statements)

References 6 publications

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“…We apply both the FVM and FDM to a pipeline network illustrated in Figure 8. Parameter settings for this pipeline network are given in [14]. Figure 8.…”

Section: Comparison Of Discretization Methodsmentioning

confidence: 99%

“…In this section, we report the performance of our numerical algorithms for the simulation of gas networks. We apply our numerical algorithms to the benchmark problems of several gas networks given in [13,16,15,14] to show the performance of our methods. All numerical experiments are performed in MATLAB 2017a on a desktop with Intel(R) Core(TM)2 Quad CPU Q8400 of 2.66GHz, 8 GB memory and the Linux 4.9.0-6-amd64 kernel.…”

Section: F11mentioning

confidence: 99%

“…However, as we move from classical to renewable energy sources in which we may use the gas pipelines to deal with flexibility from volatile energy creation, the need for fast transient simulation will increase. In recent years, research on natural gas networks focuses on a variety of topics: transient simulations [26,27,39,14,17], optimization and control [37,45,18], time splitting schemes for solving the parabolic flow equations [44], discretization methods [8,28], and model sensitivity [6] to mention a few. It is obvious that efficient simulation techniques are needed both for design and for control.…”

mentioning

confidence: 99%

“…Therefore, the inertia term can be neglected and this neglecting greatly simplifies the model, which is standard in the study of gas networks [18,14,45]. In this paper, we also use this simplification.…”

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confidence: 99%

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Efficient numerical methods for gas network modeling and simulation

Qiu

Grundel

Stoll

et al. 2020

Networks &Amp; Heterogeneous Media

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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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“…We apply both the FVM and FDM to a pipeline network illustrated in Figure 8. Parameter settings for this pipeline network are given in [14]. Figure 8.…”

Section: Comparison Of Discretization Methodsmentioning

confidence: 99%

Section: F11mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Efficient numerical methods for gas network modeling and simulation

Qiu

Grundel

Stoll

et al. 2020

Networks &Amp; Heterogeneous Media

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“…In this paper, we focus on elliptic and parabolic problems often found in the modeling of carbon nano-structures or groundwater flow (cf. [34,47]), but besides that, also hyperbolic problems have been studied intensively in the literature and cover many interesting applications like gas dynamics and traffic flow [12,13,15,16,21,24,25,27,30,53,69].…”

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confidence: 99%

Optimal Dirichlet control of partial differential equations on networks

Stoll¹,

Winkler²

2021

etna

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Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the optimal setup of the differential equation for a given desired state is a challenging numerical analysis task. In this work, we focus on the task of solving an optimization problem subject to a linear differential equation on a metric graph with the control defined on a small set of Dirichlet nodes. We discuss the discretization by finite elements and provide rigorous error bounds as well as an efficient preconditioning strategy to deal with the large-scale case. We show in various examples that the method performs very robustly.

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