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

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationComputer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings
EditorsMatthew England, Timur M. Sadykov, Werner M. Seiler, Wolfram Koepf, Evgenii V. Vorozhtsov
PublisherSpringer-Verlag GmbH and Co. KG
Pages430-450
Number of pages21
ISBN (Print)9783030268305
DOIs
Publication statusPublished - 1 Jan 2019
Event21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019 - Moscow, Russian Federation
Duration: 26 Aug 201930 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11661 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019
CountryRussian Federation
CityMoscow
Period26.08.201930.08.2019

Keywords

  • Krylov subspaces
  • Logically rectangular grids
  • Method of collocations and least squares
  • Multigrid
  • Navier–Stokes equations
  • Non-uniform grids
  • Preconditioners
  • Navier-Stokes equations

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