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Main Title: Error analysis and model adaptivity for flows in gas networks
Author(s): Stolwijk, Jeroen Johannes
Mehrmann, Volker
Type: Article
Is Part Of: 10.14279/depositonce-7650
Language Code: en
Abstract: In the simulation and optimization of natural 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 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. More- over, 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.
Issue Date: 22-Nov-2018
Date Available: 15-Jan-2020
DDC Class: 518 Numerische Analysis
Subject(s): gas network
isothermal Euler equations
algebraic approximation of Euler equations
error analysis
condition number
data uncertainty
componentwise error analysis
stochastic error analysis
Sponsor/Funder: DFG, TRR 154, Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Journal Title: Analele științifice ale Universității Ovidius Constanța. Seria Matematică
Publisher: Universitatea Ovidius din Constanţa
Publisher Place: Konstanza
Volume: 26
Issue: 2
Publisher DOI: 10.2478/auom-2018-0027
Page Start: 231
Page End: 266
EISSN: 1844-0835
ISSN: 1224-1784
Appears in Collections:FG Numerische Mathematik » Publications

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