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Main Title: Error Analysis and Model Adaptivity for Flows in Gas Networks
Author(s): Stolwijk, Jeroen J.
Mehrmann, Volker
Type: Research Paper
Abstract: In the simulation and optimization of gas flow in a pipeline network, a hierarchy of models is used that employs different formulations of the Euler equations. While the optimization is performed on piecewise linear models, the flow simulation is based on the simulation of one to three dimensional Euler equations including the temperature distributions. To decide which model class in the hierarchy is adequate to achieve a desired accuracy, this paper presents an error and perturbation analysis for a two level model hierarchy including the isothermal Euler equations in semilinear form and the stationary Euler equations in purely algebraic form. The focus of the work is on the effect of data uncertainty, discretization and rounding errors in the numerical simulation of these models and their interaction. Two simple discretization schemes for the semilinear model are compared with respect to their conditioning and temporal stepsizes are determined for which a well-conditioned problem is obtained. The results are based on new componentwise relative condition numbers for the solution of nonlinear systems of equations. Moreover, the model error between the semilinear and the algebraic model is computed, the maximum pipeline length is determined for which the algebraic model can be used safely, and a condition is derived for which the isothermal model is adequate.
Subject(s): gas network
isothermal Euler equations
error analysis
condition number
data uncertainty
componentwise error analysis
stochastic error analysis
Issue Date: 4-Jan-2017
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65M15 Error bounds
35Q35 Other equations arising in fluid mechanics
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2017, 02
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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