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Model and Discretization Error Adaptivity within Stationary Gas Transport Optimization

Volker Mehrmann(mehrmann***at***math.tu-berlin.de)
Martin Schmidt(mar.schmidt***at***fau.de)
Jeroen J. Stolwijk(stolwijk***at***math.tu-berlin.de)

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

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Network Optimization

Category 3: Applications -- Science and Engineering

Citation:

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Entry Submitted: 12/06/2017
Entry Accepted: 12/06/2017
Entry Last Modified: 12/06/2017

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