Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - THES
AU - Stolwijk, Jeroen Johannes
PY - 2019
TI - Error analysis and adaptive control for gas flow in networks
T2 - Technische Universität Berlin
DO - 10.14279/depositonce-7650
UR - http://dx.doi.org/10.14279/depositonce-7650
PB - Technische Universität Berlin
M3 - Doctoral Thesis
CY - Berlin
LA - en
AB - In this thesis, uniform estimators are derived for the different errors that a numerical solution could contain, namely modeling, discretization, iteration, data uncertainty, and rounding errors. Subsequently, the errors are adaptively controlled on a network in order to bring the total error below a prescribed tolerance while keeping the computational cost low. As example problems, the simulation and optimization of gas flow through pipeline networks are considered. The gas flow is modeled by the Euler equations of fluid dynamics, which are a system of hyperbolic partial differential equations. This system is complemented by suitable initial, boundary, and coupling conditions and discretized using different schemes, e.g., the implicit box scheme, which is an effective discretization method for transient gas flow models. Due to the high computational complexity of this system of partial differential equations, simplifications are often made using appropriate assumptions, resulting in a model hierarchy. Purely algebraic models may be used in parts of the network with low gas dynamics, whereas more involved models should be used, e.g., right after a compressor. In this thesis, an error and sensitivity analysis for many models in this hierarchy is performed. Since the modeling and discretization errors have already been extensively studied in the literature, the first focus lies on the rounding and data uncertainty errors. These errors are computed via a backward error analysis for the obtained nonlinear systems of equations. For this, a novel componentwise condition number is introduced and the advantage over the classical normwise condition number is demonstrated. The developed sensitivity analysis is applied, inter alia, on an exemplary Y-shaped gas network, where the effect of changing boundary conditions on the network state is investigated. In order to find a convenient trade-off between accuracy and computational complexity, the different errors on every pipe are adaptively controlled. For this, new Greedy-like spatial/temporal/model refinement strategies are developed, which have a network overview and take the behavior of the gas better into account than the strategy that is currently implemented in the gas flow simulation software ANACONDA. Both a synthetic and a realistic experiment show that the new strategies significantly reduce the computational cost as compared to the current refinement strategy while maintaining the same error tolerance. Moreover, it is shown that adaptive error control (using bulk criteria, which are frequently employed in the adaptive finite element method) can also be applied within an optimization algorithm, which again results in a reduction of the computational cost. It is proven that, also when one allows for coarsenings, an epsilon-feasible solution is obtained after a finite number of iterations. Note that the developed error estimators and adaptive error control techniques are not limited to gas networks, but can also be applied to, e.g., water, electricity, or traffic networks.
KW - Euler equations of fluid dynamics
KW - componentwise condition number
KW - backward error analysis
KW - adaptive error control
KW - nonlinear programming
KW - Euler-Gleichungen der Strömungsmechanik
KW - komponentenweise Konditionszahl
KW - Rückwärtsfehleranalyse
KW - adaptive Fehlersteuerung
KW - nichtlineare Programmierung
ER -