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 -