vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2019-2-2-54-66vmait-59Research ArticleСтатьиПовышение гладкости численного решения моделирования задач гидродинамики на прямоугольных сеткахLinear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation errorhttps://orcid.org/0000-0002-8323-6005ЧистяковАлександр ЕвгеньевичChistyakovAlexander Evgenievich

Чистяков Александр Евгеньевич, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), доктор физико-математических наук, доцент

Chistyakov Alexander Evgenievich, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Associate professor

https://orcid.org/0000-0003-4629-1002АтаянАся МихайловнаAtayanAsya Mikhailovna

Атаян Ася Михайловна, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), аспирант

Atayan Asya Mikhailovna, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), postgraduate student

Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1)РоссияDon State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation)Russian FederationДонской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1)РоссияDon State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation)Russian Federation2019280320233259Copyright © Чистяков А.Е., Атаян А.М., 20232023Чистяков А.Е., Атаян А.М.Chistyakov A.E., Atayan A.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/59

Для решения задачи переноса предлагается использовать схему, основанную на линейной комбинации схемы «Кабаре» и «Крест» с весовыми коэффициентами, полученными из условия минимизации порядка погрешности аппроксимации. Оценка погрешности аппроксимации предложенной разностной схемы показывает, что для малых чисел Куранта предпочтительнее использовать эту схему, погрешность аппроксимации которой равна O(ch2), где константа c значительно меньше единицы, чем исходные схемы «Кабаре» и «Крест», погрешности аппроксимации которых равны O(h2). Предложенная модификация разностной схемы «Крест» эффективна для решения задачи диффузии-конвекции в диапазоне чисел пекле 2≤Pe≤20.

In order to solve the transfer problem, it is proposed to use the scheme based on a linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficientsobtained by minimizing the approximation error. The estimate of the approximation error of the proposed difference scheme shows that, for small Courant numbers, this scheme whose approximation error is O(ch2), where the constant c is significantly less than unity, is preferable to use than the original Upwind and Standard Leapfrog schemes whose approximation errors are O(h2). The proposed modification of the Upwind Leapfrog difference scheme is effective for solving the diffusion-convection problem in the range of Peclet numbers 2≤Pe≤20.

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