Численный анализ математической модели динамики турбулентного течения многофазной среды в сетеподобных объектах
Работая с нашим сайтом, вы даете свое согласие на использование файлов cookie. Это необходимо для нормального функционирования сайта, показа целевой рекламы и анализа трафика. Статистика использования сайта отправляется в «Яндекс» и «Google»
Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

Numerical analysis of the mathematical model of the turbulent flow dynamics of a multiphase medium in network-like objects

idHoang V. Part A.A.   Perova I.V.  

UDC 517.977.56
DOI: 10.26102/2310-6018/2023.41.2.006

  • Abstract
  • List of references
  • About authors

This paper presents methods of mathematical analysis used to solve the applied problems of the theory of transport of solid media – thermal flows and viscous liquids in network-like objects. The initial-boundary problem for the Navier-Stokes system, which lies at the basis of the mathematical description of the so-called turbulent transport processes of Newtonian liquids with a given viscosity, is defined and studied. It is assumed that the liquid has a complex internal rheology and is a multi-phase continuous medium. The distinctive feature of the process under consideration is the absence of a classical differential equation at the node points of the network-like area (the surfaces of mutual adhesion of subdomains). Sufficient conditions for the unique weak solvability of the initial-boundary problem are presented, which are obtained by the classical analysis of approximations of the exact solution by means of a priori estimates derived from the energy inequality for norms of solutions of the Navier-Stokes equation. An optimization problem, which is natural in the analysis of transport processes of continuous media on a network-like carrier, is considered. The state spaces of the Navier-Stokes system, spaces of controls and observations, for which the uniqueness of the solution of the optimization problem is proved, are indicated. The suggested approach and corresponding methods are equipped with the necessary algorithm and illustrated by the examples of numerical analysis of test problems. The basis of the analysis lies in the classical approach to studying mathematical models of transport processes of continuous media. The paper is aimed at developing qualitative and approximate methods for investigating mathematical models of various types of continuous media transport.

1. Lubary J.A. On the geometric and algebraic multiplicities for eigenvalue problems on graphs. Lecture Notes in Pure and Applied Mathematics. 2001;219:135–146.

2. Nicaise S., Penkin O. Relationship between the lower frequense spectrum of plates and networks of beams. Mathematical Methods in the Applied Sciences. 2000;23(16):1389–1399. DOI: 10.1002/1099-1476(20001110)23:16<1389::aid-mma171>3.0.co;2-k.

3. Von Below J. Sturm-Liouville eigenvalue problems on networks. Mathematical Methods in the Applied Sciences. 1988;10(4):383–395. DOI: 10.1002/mma.1670100404.

4. Dekoninck B., Nicaise S. The eigenvalue problem for networks of beams. Linear Algebra and its Applications. 2000;314(1–3):165–189. Available from: https://www.sciencedirect.com/science/article/pii/S002437950000118X?via%3Dihub (accessed on 27.02.2023).

5. Sergeev S.M., Raijhelgauz L.B., Hoang V.N., Panteleev I.N. Modeling unbalanced systems in network-like oil and gas processes. Journal of Physics: Conference Series. 2020;1679(2):022015. Available from: https://iopscience.iop.org/article/10.1088/1742-6596/1679/2/022015 (accessed on 27.02.2023).

6. Provotorov V.V. Sobstvennyye funktsii krayevykh zadach na grafakh i prilozheniya. Voronezh. Nauchnaya kniga; 2008. 247 p. (In Russ.).

7. Zhabko A.P., Nurtazina K.B., Provotorov V.V. About one approach to solving the inverse problem for parabolic equation. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes. 2019;15(3):323–336. Available from: https://dspace.spbu.ru/handle/11701/16384 (accessed on 27.02.2023).

8. Baranovskii E.S. Steady flows of an Oldroyd fluid with threshold slip. Communications on Pure and Applied Analysis. 2019;18(2):735–750. DOI: 10.3934/cpaa.2019036.

9. Baranovskii E.S. Existence results for regularized equations of second-grade fluids with wall slip. Electronic Journal of Qualitative Theory of Differential Equations. 2015;(91):1–12. Available from: http://real.mtak.hu/32263/ (accessed on 27.02.2023).

10. Artemov M.A., Baranovskii E.S. Solvability of the Boussinesq approximation for water polymer solutions. Mathematics. 2019;7(7). Article ID 611. Available from: https://www.mdpi.com/2227-7390/7/7/611 (accessed on 27.02.2023).

Hoang Van Nguyen


Voronezh State University

Voronezh, Russian Federation

Part Anna Aleksandrovna
Candidate of Physical and Mathematical Sciences

Voronezh State University

Voronezh, Russian Federation

Perova Irina Vasilievna

Voronezh State University

Voronezh, Russian Federation

Keywords: transfer of hydroflows, network carrier, optimization problem, algorithms, numerical analysis

For citation: Hoang V. Part A.A. Perova I.V. Numerical analysis of the mathematical model of the turbulent flow dynamics of a multiphase medium in network-like objects. Modeling, Optimization and Information Technology. 2023;11(2). Available from: https://moitvivt.ru/ru/journal/pdf?id=1326 DOI: 10.26102/2310-6018/2023.41.2.006 (In Russ).


Full text in PDF

Received 08.03.2023

Revised 21.03.2023

Accepted 14.04.2023

Published 25.04.2023