A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation

Evgenii V. Vorozhtsov, Vasily P. Shapeev

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

To increase the accuracy of computations by the method of collocations and least squares (CLS) a generalization of this method is proposed for the case of a non-uniform logically rectangular grid. The main work formulas of the CLS method on non-uniform grid, including the formulas implementing the prolongation operator on a non-uniform grid at the use of a multigrid complex are obtained with the aid of the computer algebra system (CAS) Mathematica. The proposed method has been applied for the numerical solution of two-dimensional stationary Navier–Stokes equations governing the laminar flows of viscous incompressible fluids. On a smooth test solution, the application of a non-uniform grid has enabled a 47-fold reduction of the solution error in comparison with the uniform grid case. At the solution of the problem involving singularities – the lid-driven cavity flow – the error of the solution obtained by the CLS method was reduced by the factors from 2.65 to 3.05 depending on the Reynolds number value.

Язык оригиналаанглийский
Название основной публикацииComputer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings
РедакторыMatthew England, Timur M. Sadykov, Werner M. Seiler, Wolfram Koepf, Evgenii V. Vorozhtsov
ИздательSpringer-Verlag GmbH and Co. KG
Страницы430-450
Число страниц21
ISBN (печатное издание)9783030268305
DOI
СостояниеОпубликовано - 1 янв 2019
Событие21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019 - Moscow, Российская Федерация
Продолжительность: 26 авг 201930 авг 2019

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том11661 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

Конференция

Конференция21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019
СтранаРоссийская Федерация
ГородMoscow
Период26.08.201930.08.2019

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