Theoretical Analysis on Numerical Error of MOC-based Time-line Method Predicting Pipe Flows and Grid Generation of Combined Time-line Method

Abstract

An approximate solution of describing numerical errors due to the time-line interpolations (numerical damping and dispersion) is analytically derived, which gives a theoretical basis of the combined time-line method of efficiently predicting steady and unsteady flows in pipelines. The accuracy of this solution has been proved to be extremely high through comparisons with numerical solutions. General properties of the numerical errors are investigated based on the analytic solution. The algorithm of designing optimal time step sizes and gridsystems is improved to simpler and more economical one through incorporating the analytic expression of the numerical error into the algorithm.