Gas flow in pipeline networks

Banda, Mapundi K.; Herty, Michaël; Klar, Axel

doi:10.3934/nhm.2006.1.41

Cited by 181 publications

(226 citation statements)

References 16 publications

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“…This twodimensional view is now used to obtain boundary conditions for (4). As in the theory presented in [5] for the equations (4), we consider constant initial data ρ 0 k , u 0 k for k = 1, 2 and 3. This data is used to define initial values for equation (12) as…”

Section: Numerical Methods and Solution Proceduresmentioning

confidence: 99%

“…Therefore, the discussion can be equivalently applied to gas and water flows in networks. Currently, different conditions have been proposed and discussed in the case of gas networks [4,5,7,8]. For water networks extensive studies have been done in [6,13,17,18] among others.…”

Section: Introductionmentioning

confidence: 99%

“…It has been proven that under suitable assumptions this procedure gives existence, uniqueness and Lipschitz dependence on the initial data for general 2×2-system of conservation laws and for rather general coupling conditions, we refer the reader to [9] for more details. The results of this discussion can be used in modified Riemann solvers for numerical purposes, see [5,4,1,21] for a situation of two coupled gas pipes with different flux functions. This approach is similar to the solution of initial-boundary value problems for hyperbolic systems with the difference being that in the present case we additionally have to satisfy some algebraic conditions.…”

mentioning

confidence: 99%

“…This is the case for the mathematical discussion as well as the case in all engineering applications [32]. Well-posedness of the different coupling conditions has been analyzed by various authors and we can only give an incomplete list of references [5,9,11,14,24] and offer only a partial discussion of some results. Nowadays, there exists results in two directions.…”

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Assessment of coupling conditions in water way intersections

Herty

Seaı̈d

2012

Numerical Methods in Fluids

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Publisher's copyright statement:his is the epted version of the following rti leX rertyD wF nd e ¤ %dD wF @PHIQAD essessment of oupling onditions in w ter w y interse tionsF sntern tion l tourn l for xumeri l wethods in pluidsD UI @IIAX IRQVEIRTHD whi h h s een pu lished in (n l form t httpXGGdxFdoiForgGIHFIHHPG)dFQUIWF his rti le m y e used for nonE ommer i l purposes in ord n e ith iley erms nd gonditions for selfE r hivingFAdditional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. SUMMARYWe present a numerical assessment of coupling conditions in T-junction for water flow in open canals. The mathematical model is based on the well-established shallow water equations for open channel flows. In the present work, the emphasis is given to the description of coupling conditions at canalto-canal intersections. The accurate prediction of these coupling conditions is essential in order to achieve good performance and reliable numerical simulations of water canals in networks. There is exists several theoretical results for coupling conditions in a reduced geometry. The purpose of our work is to numerically verify these conditions for different water flow regimes. More precisely, we consider a local zooming of the T-junction resulting in a two-dimensional flow problem at the canals intersection. A high-order non-oscillatory method is used for solving the governing two-dimensional equations and the water flow solutions are space-averaged over the junction areas. The obtained numerical results are thereafter, used for verification and comparison with the theoretical results. Verifications are conducted for two types of junctions namely the 1-to-2 and 2-to-1 situations.

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Section: Numerical Methods and Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Assessment of coupling conditions in water way intersections

Herty

Seaı̈d

2012

Numerical Methods in Fluids

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“…3 The corresponding parameter value is b = 500 The properties of the corresponding specification of the permeabilitities γ i (t) are as follows:…”

Section: 3mentioning

confidence: 99%

Self-Organized Network Flows

Helbing

Siegmeier²,

Lämmer³

2012

Lecture Notes in Mathematics

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Abstract.A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and load-dependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find self-organized oscillations in the flows similar to the operation of traffic lights.

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Simulation of transient gas flow at pipe‐to‐pipe intersections

Herty

Seaı̈d

2007

Numerical Methods in Fluids

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SUMMARYWe numerically investigate a well-established mathematical model for gas flow in pipeline networks. The emphasis is given to the description of coupling conditions at pipe-to-pipe intersections. The accurate prediction of these coupling conditions is essential in order to achieve good performance and reliable numerical simulations of network simulations. Nowadays, a variety of theoretical results for a reduced geometry exists. We conduct a numerical simulation of the two-dimensional representation at a pipe intersection. The results are used for verification and comparison with known theoretical results. High-order and non-oscillatory discretizations are used for solving the governing equations of gas flow. Verifications are conducted for two types of junctions to analyse the most adequate coupling conditions.

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Gas flow in pipeline networks

Cited by 181 publications

References 16 publications

Assessment of coupling conditions in water way intersections

Assessment of coupling conditions in water way intersections

Self-Organized Network Flows

Simulation of transient gas flow at pipe‐to‐pipe intersections

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