Multifunctional transformation method in flow modelling

Abstract

In the paper we consider a new approach for solution of PD E ’s generating by transient gas flow networks of pipelines. In particular, the fundamental solution representation for the considered problem is based on exploiting the so-called canonical system formed by the collection of the eigenfunctions for the underlying operator and its adjoint. This canonical system lies in the base of the developed multifunctional integral transformation for spatial variables that is core of operational calculus for PDE’s. The main objective is to present a new approach that can be used then to construct the parallel numerical method which meets the suitable accuracy and relatively small computation time.