TY - INPR A1 - Stolwijk, Jeroen J. A1 - Mehrmann, Volker T1 - Error Analysis and Model Adaptivity for Flows in Gas Networks N2 - 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. KW - gas network KW - isothermal Euler equations KW - error analysis KW - condition number KW - data uncertainty Y1 - 2017 ER - TY - INPR A1 - Mehrmann, Volker A1 - Stolwijk, Jeroen J. T1 - Error Analysis for the Euler Equations in Purely Algebraic Form N2 - 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. KW - error analysis KW - measurement error KW - condition number KW - backward error KW - statistical analysis Y1 - 2015 ER -