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A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation. / Vorozhtsov, Evgenii V.; Shapeev, Vasily P.

Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. ed. / Matthew England; Timur M. Sadykov; Werner M. Seiler; Wolfram Koepf; Evgenii V. Vorozhtsov. Springer-Verlag GmbH and Co. KG, 2019. p. 430-450 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11661 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Vorozhtsov, EV & Shapeev, VP 2019, A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation. in M England, TM Sadykov, WM Seiler, W Koepf & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11661 LNCS, Springer-Verlag GmbH and Co. KG, pp. 430-450, 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, Moscow, Russian Federation, 26.08.2019. https://doi.org/10.1007/978-3-030-26831-2_28

APA

Vorozhtsov, E. V., & Shapeev, V. P. (2019). A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation. In M. England, T. M. Sadykov, W. M. Seiler, W. Koepf, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings (pp. 430-450). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11661 LNCS). Springer-Verlag GmbH and Co. KG. https://doi.org/10.1007/978-3-030-26831-2_28

Vancouver

Vorozhtsov EV, Shapeev VP. A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation. In England M, Sadykov TM, Seiler WM, Koepf W, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. Springer-Verlag GmbH and Co. KG. 2019. p. 430-450. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-26831-2_28

Author

Vorozhtsov, Evgenii V. ; Shapeev, Vasily P. / A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation. Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. editor / Matthew England ; Timur M. Sadykov ; Werner M. Seiler ; Wolfram Koepf ; Evgenii V. Vorozhtsov. Springer-Verlag GmbH and Co. KG, 2019. pp. 430-450 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

BibTeX

@inproceedings{2309a2f6ebc84a26a708ad9a02d9526f,
title = "A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation",
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.",
keywords = "Krylov subspaces, Logically rectangular grids, Method of collocations and least squares, Multigrid, Navier–Stokes equations, Non-uniform grids, Preconditioners, Navier-Stokes equations",
author = "Vorozhtsov, {Evgenii V.} and Shapeev, {Vasily P.}",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019 ; Conference date: 26-08-2019 Through 30-08-2019",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-26831-2_28",
language = "English",
isbn = "9783030268305",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer-Verlag GmbH and Co. KG",
pages = "430--450",
editor = "Matthew England and Sadykov, {Timur M.} and Seiler, {Werner M.} and Wolfram Koepf and Vorozhtsov, {Evgenii V.}",
booktitle = "Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings",
address = "Germany",

}

RIS

TY - GEN

T1 - A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation

AU - Vorozhtsov, Evgenii V.

AU - Shapeev, Vasily P.

N1 - Publisher Copyright: © 2019, Springer Nature Switzerland AG.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Krylov subspaces

KW - Logically rectangular grids

KW - Method of collocations and least squares

KW - Multigrid

KW - Navier–Stokes equations

KW - Non-uniform grids

KW - Preconditioners

KW - Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=85071417071&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-26831-2_28

DO - 10.1007/978-3-030-26831-2_28

M3 - Conference contribution

AN - SCOPUS:85071417071

SN - 9783030268305

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 430

EP - 450

BT - Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings

A2 - England, Matthew

A2 - Sadykov, Timur M.

A2 - Seiler, Werner M.

A2 - Koepf, Wolfram

A2 - Vorozhtsov, Evgenii V.

PB - Springer-Verlag GmbH and Co. KG

T2 - 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019

Y2 - 26 August 2019 through 30 August 2019

ER -

ID: 21489283