kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2023-20-4-85-96kaz29-877Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESЧисленное моделирование существенно дозвуковых течений сжимаемого газаNumerical modeling of essentially subsonic flows of compressible gashttps://orcid.org/0000-0003-1548-7061МанаповаА. К.МanapovaA.  

Манапова Айнур Қабдешқызы, Магистр прикладной математики и информатики, сениор-лектор

ул. Ахметова, 44, 050039, г. Алматы

Manapova Ainur, Master of applied mathematics and computer science, Senior Lecturer

050039, Almaty

manapova.a.k.math@gmail.comhttps://orcid.org/0000-0003-4360-3728БекетаеваА. О.BeketaevaA.

Бекетаева Асель Орозалиевна, Доктор физико-математических наук, главный научный сотрудник

ул. Пушкина, 125, 050010, г. Алматы

Beketaeva Assel, Доктор физико-математических наук, Главный научный сотрудник института математики и математического моделирования

ул. Пушкина, 125, 050010, Almaty

azimaras10@gmail.comhttps://orcid.org/0000-0003-4874-5418МакаровВ. В.MakarovV. 

Макаров Вадим Владимирович, Кандидат технических наук, ведущий научный сотрудник

ул. Профсоюзная, 65, 117997, г. Москва

Makarov Vadim, Кандидат технических наук, Ведущий научный сотрудник

ул. Профсоюзная, 65, 117997, Moscow

makfone@mail.ruАкадемиия гражданской авиацииКазахстанCivil Aviation AcademyKazakhstanИнститут математики и математического моделирования КН МОН РККазахстанInstitute of mathematics and mathematical modeling CS МES RKKazakhstanИнститут проблем управления РАН; Национальный исследовательский ядерный университет «МИФИ»РоссияInstitute of control sciences RAS; National research nuclear university «MEPhI»Russian Federation2023121220232048596Copyright © Манапова А.К., Бекетаева А.О., Макаров В.В., 20232023Манапова А.К., Бекетаева А.О., Макаров В.В.Мanapova A., Beketaeva A., Makarov V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/877

Предлагается новый метод решения существенно дозвуковых течений, который представляет собой значительный шаг в области численного моделирования течений на основе системы уравнений Навье-Стокса. В методе используется ENO (Essentially Non-Oscillatory) схема третьего порядка точности, которая обеспечивает более высокую точность при расчетах течений с низкой скоростью звука. Одной из ключевых особенностей этого метода является введение параметров обезразмеривания. Эти параметры позволяют адаптировать уравнения Навье-Стокса к различным физическим условиям и избежать жесткости уравнений, что часто встречается в задачах численного моделирования. Это делает метод более гибким и применимым к разнообразным инженерным и физическим задачам. Для проверки и апробации данной методики проводятся вычисления для двух важных задач – течения внутри каверны и течения Пуазейля. Рассматривается значение числа Рейнольдса, Re=100, а также различные размеры вычислительных сеток. Полученные результаты сравниваются с экспериментальными данными, и наблюдается высокая степень согласования между моделью и реальными явлениями. Это свидетельствует об эффективности и точности предложенного метода в решении сложных течений в различных инженерных и физических задачах.

A new method for solving essentially subsonic flows is proposed, which represents a significant step in the field of numerical modeling of flows based on the Navier-Stokes system of equations. The method uses an ENO (Essentially Non-Oscillatory) scheme of third order accuracy, which provides higher accuracy when calculating flows with low speed of sound. One of the key features of this method is the introduction of nondimensionalization parameters. These parameters make it possible to adapt the Navier-Stokes equations to different physical conditions and avoid the rigidity of the equations, which is often encountered in numerical modeling problems. This makes the method more flexible and applicable to a variety of engineering and physical problems. To check and approbate this technique, calculations are carried out for two important problems - flow inside a cavern and Poiseuille flow. The value of the Reynolds number, Re=100, as well as various sizes of computational grids are considered. The obtained results are compared with experimental data, and a high degree of agreement between the model and real phenomena is observed. This indicates the effectiveness and accuracy of the proposed method in solving complex flows in various engineering and physical problems.

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The authors declare that there are no conflicts of interest present.