@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",

}