Title: Adjoint-based control of model and discretisation errors for gas flow in networks

Authors: Pia Domschke, Oliver Kolb, Jens Lang

Addresses: Department of Mathematics, Technische Universitat Darmstadt Dolivostr. 15, D-64293 Darmstadt, Germany; Center of Smart Interfaces, Technische Universitat Darmstadt Petersenstr. 30, D-64287 Darmstadt, Germany; Graduate School Computational Engineering, Technische Universitat Darmstadt Dolivostr. 15, D-64293 Darmstadt, Germany. ' Department of Mathematics, Technische Universitat Darmstadt Dolivostr. 15, D-64293 Darmstadt, Germany; Center of Smart Interfaces, Technische Universitat Darmstadt Petersenstr. 30, D-64287 Darmstadt, Germany; Graduate School Computational Engineering, Technische Universitat Darmstadt Dolivostr. 15, D-64293 Darmstadt, Germany. ' Department of Mathematics, Technische Universitat Darmstadt Dolivostr. 15, D-64293 Darmstadt, Germany; Center of Smart Interfaces, Technische Universitat Darmstadt Petersenstr. 30, D-64287 Darmstadt, Germany; Graduate School Computational Engineering, Technische Universitat Darmstadt Dolivostr. 15, D-64293 Darmstadt, Germany

Abstract: We are interested in the simulation and optimisation of gas transport in networks. The gas flow through pipes can be modelled on the basis of the (isothermal) Euler equations. Further network components are described by purely algebraic equations. Depending on the data and the resulting network dynamics, models of different fidelity can be used in different regions of the network. Using adjoint techniques, we derive model and discretisation error estimators. Here, we apply a first-discretise approach. Based on the time-dependent structure of the considered problems, the adjoint systems feature a special structure and therefore allow for an efficient solution. A strategy that controls model and discretisation errors to maintain the accuracy of the solution is presented. We provide (technical) details of our implementation and give numerical results.

Keywords: model adaptivity; adjoint-based error control; model error estimator; discretisation error estimator; first-discretise approach; gas flow; Euler equations; gas transport; networks; mathematical modelling; numerical simulation; model errors; discretisation errors; gas pipes; network dynamics.

DOI: 10.1504/IJMMNO.2011.039427

International Journal of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2 No.2, pp.175 - 193

Published online: 26 Mar 2015 *

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