Локально-одномерный метод для уравнения переноса сплошной среды с распределенными параметрами на сетеподобной области
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Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

Locally one-dimensional method for the transfer equation of a continuous medium with distributed parameters on a network-like domain

Tran D.  

UDC 517.977.56
DOI: 10.26102/2310-6018/2022.37.2.008

  • Abstract
  • List of references
  • About authors

The paper considers a wide range of issues related to the solution of an initial-boundary value problem for a parabolic partial differential equation with a multidimensional space variable belonging to the Euclidean space and changing on a network-like domain. The mathematical model describing the process of transferring a continuous medium over a network carrier is determined by the formalism of the initial-boundary value problem. An idea that has become classical is further developed for the case when a network-like region is a directed bounded graph, i.e., a collection of a finite number of segments connected to each other by means of end points. The study employs classical approximations of evolutionary differential equations of the 2-nd order as well as non-classical approximations of differential relations illustrated by generalized Kirchhoff conditions at the branching points of a network-like region (nodal points of the region). When using difference approximations of the initial-boundary value problem operator, the approximation error and stability conditions for the difference scheme are established. The characteristic properties of the locally one-dimensional method and the sweep method utilized to solve the stated problem are studied. An algorithm for the numerical solution of the stated problem is proposed, a computer program is designed, and a computational experiment is carried out on a series of applied problems. The findings are of interest in the analysis of applied problems of multiphase continuum media transfer along network-like 3D carriers.

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Tran Duy

Email: tranduysp94@gmail.com

Voronezh State University, Voronezh, Russian Federation

Voronezh, Russia

Keywords: initial-boundary value transfer problem, network (directed graph), continuous medium transfer, difference scheme, locally one-dimensional method

For citation: Tran D. Locally one-dimensional method for the transfer equation of a continuous medium with distributed parameters on a network-like domain. Modeling, Optimization and Information Technology. 2022;10(2). Available from: https://moitvivt.ru/ru/journal/pdf?id=1141 DOI: 10.26102/2310-6018/2022.37.2.008 (In Russ).

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Full text in PDF

Received 15.03.2022

Revised 19.04.2022

Accepted 28.04.2022

Published 11.05.2022