Numerical Error in Method of Characteristics with Weighting Function-Based Model for Small Amplitude Wave in Gas Pipeline

The method of characteristics is suitable to calculate small amplitude wave in gas pipeline. The method is superior in a case that the boundary conditions have many frequency components, while requires a computation of unsteady friction terms. The unsteady friction terms include convolution integral of which calculation is time-consuming. Reduction of the computation load with maintenance of its accuracy, which is essential for a practical computation, requires a weighting function-based (WFB) approximation which approximates the weighting functions by sums of exponential terms, and of convolution integrals. However, even the WFB model contains approximation errors which sometimes cause computation error. The approximation errors in liquid pipeline have been evaluated in Fourier domain. However, the errors in gas pipeline have not been evaluated. In this paper, we present a discussion and quantification of the numerical errors that occur when using the method for the simulation of small amplitude wave in gas pipeline. Comparisons of numerical error caused by approximations are made in the Fourier domain where exact solutions can be determined.