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Error Analysis for the Euler Equations in Purely Algebraic Form

  • The presented work contains both a theoretical and a statistical error analysis for the Euler equations in purely algebraic form, also called the Weymouth equations or the temperature dependent algebraic model. These equations are obtained by performing several simplifications of the full Euler equations, which model the gas flow through a pipeline. The theoretical analysis is executed by first calculating the backward error and then the individual relative condition numbers. This error analysis results in a statement about the maximum pipeline length such that the algebraic model can be used safely. The statistical analysis is performed using both a Monte Carlo Simulation and the Univariate Reduced Quadrature Method and is used to illustrate and confirm the obtained theoretical results.

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Author:Volker Mehrmann, Jeroen J. Stolwijk
Document Type:Preprint
Language:English
Date of Publication (online):2015/06/03
Year of first Publication:2015
Release Date:2016/05/03
Tag:backward error; condition number; error analysis; measurement error; statistical analysis
Page Number:27
Institutes:Technische Universität Berlin
Subprojects:B03