Discrete-time stabilization of wave phenomena engineering of network-like continuum transfer processes

Abstract

Abstract This work is a natural continuation of the authors’ research of flow phenomena in the direction of increasing the dimension of the network-like region of change in the spatial variable. The possibility of practical use of the stability analysis of the differential-difference scheme to solve the problem of stabilization of wave phenomena in the engineering of the process of transfer of continuous media through network-like carriers (pipelines, gas and oil pipelines, industrial carriers of gas and petroleum products) is shown. Namely, if the scheme is stable, then sufficiently small changes in the initial data of the mathematical model of the process under study entail small changes in the solution of the difference problem, i.e. in practice do not lead to undesirable consequences; if the scheme is unstable, then small changes in the initial data can lead to arbitrarily large changes in the solution. During the operation of the above-mentioned industrial structures, wave phenomena inevitably arise, the consequence of which are various kinds of instabilities, entailing destruction of one or another nature. The results obtained are used in the digitalization of modern technological processes for the movement of liquid media and gases.