Gas Pipeline Models Revisited: Model Hierarchies, Nonisothermal Models, and Simulations of Networks

Brouwer, Jens; Gasser, Ingenuin; Herty, Michaël

doi:10.1137/100813580

Cited by 110 publications

(121 citation statements)

References 21 publications

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“…They consist of the continuity equation, the balance of moments and the energy equation. The full set of equations is given by (see [1] [2] [3] [4]). Let ρ denote the density, v the velocity of the gas and p the pressure.…”

Section: Modeling Of Gas Flow In a Single Pipementioning

confidence: 99%

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

Leugering¹

2017

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We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.

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Section: Modeling Of Gas Flow In a Single Pipementioning

confidence: 99%

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

Leugering¹

2017

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“…Therefore we consider the simplest possible network, three edges and two nodes connected as depicted in Figure 4. As coupling conditions we use the impulse-flux coupling (7). For the initial data we need smooth functions along the edges, which simultaneously simultaneously fulfill all the coupling conditions at the junctions and all its temporal derivatives (11) ρ i (x, 0) = 1 2 cos(2πx) + 1 i = 1, 2, 3 ,…”

Section: Rates Of Convergencementioning

confidence: 99%

“…Networks of hyperbolic conservation laws occur in many applications such as the human circulatory system [1,2,3,4], gas pipelines [5,6,7], water [8,9,10,11] and road networks [12,13]. For all these applications accurate and stable numerical methods are needed.…”

Section: Introductionmentioning

confidence: 99%

ADER schemes and high order coupling on networks of hyperbolic conservation laws

Borsche

Kall

2014

Journal of Computational Physics

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In this article we present a method to extend high order finite volume schemes to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if stated by the coupling conditions. Several numerical examples confirm the benefits of a high order coupling procedure for high order accuracy and stable shock capturing.

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“…For pipes, theoretical studies include the controllability and stabilization of the governing system of partial differential equations, the Euler equations (cf. Banda and Herty 2008;Banda et al 2006;Brouwer et al 2011;Gugat et al 2015). The best-investigated problem for compressor stations is the one considered in this paper, which is of nonconvex MINLP type: minimum cost operation under given boundary conditions (Carter 1996;Carter et al 1994;Jeníček and Králik 1993;Osiadacz 1980;Wright et al 1998).…”

Section: Introductionmentioning

confidence: 99%

Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

et al. 2016

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When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to nonconvex mixed-integer nonlinear optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several continuous reformulations of the problem. The applicability and relevance of different model formulations, especially of those without discrete variables, is demonstrated by a computational study on both academic examples and real-world instances. In addition, we provide preliminary computational results for an entire network.

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Gas Pipeline Models Revisited: Model Hierarchies, Nonisothermal Models, and Simulations of Networks

Cited by 110 publications

References 21 publications

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

ADER schemes and high order coupling on networks of hyperbolic conservation laws

Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

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