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Preprint 11-2017

Model and Discretization Error Adaptivity within Stationary Gas Transport Optimization

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Author(s) : Volker Mehrmann , Martin Schmidt , Jeroen J. Stolwijk

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 11-2017

MSC 2000

35Q35 Other equations arising in fluid mechanics
65G99 None of the above, but in this section

Abstract :
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical examples.

Keywords : Gas transport optimization, Isothermal stationary Euler equations, Model hierarchy, Adaptive error control, Marking strategy

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