Adjoint calculus for optimization of gas networks

Michael Herty; Veronika Sachers; Michael Herty; Veronika Sachers

doi:10.3934/nhm.2007.2.733

Networks and Heterogeneous Media

2007, Volume 2, Issue 4: 733-750. doi: 10.3934/nhm.2007.2.733

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Adjoint calculus for optimization of gas networks

Michael Herty ^{1
,},
Veronika Sachers ^{1
,}

1.
Technische Universität Kaiserslautern, Fachbereich Mathematik, Postfach 3049, D-67653 Kaiserslautern

Received: 01 March 2007 Revised: 01 August 2007
Primary: 76N25; Secondary: 35Lxx.

We consider an optimization problem arising in the context of gas transport in pipe networks. To compensate the pressure loss due to friction and to guarantee a desired (time dependent) outflow profile, compressor stations are included in the network. These compressor stations are relatively cost-intensive, so that a cost effective control is required. In the presented model the compressors are special vertices of the network. We derive an adjoint calculus for gas networks to solve the optimization problem and prove well–posedness of forward and adjoint coupling conditions. Furthermore, numerical examples illustrate the obtained results.
- Isothermal Euler equations,
- Networks,
- Flow control
Citation: Michael Herty, Veronika Sachers. Adjoint calculus for optimization of gas networks[J]. Networks and Heterogeneous Media, 2007, 2(4): 733-750. doi: 10.3934/nhm.2007.2.733

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Abstract

We consider an optimization problem arising in the context of gas transport in pipe networks. To compensate the pressure loss due to friction and to guarantee a desired (time dependent) outflow profile, compressor stations are included in the network. These compressor stations are relatively cost-intensive, so that a cost effective control is required. In the presented model the compressors are special vertices of the network. We derive an adjoint calculus for gas networks to solve the optimization problem and prove well–posedness of forward and adjoint coupling conditions. Furthermore, numerical examples illustrate the obtained results.
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