Numerical comparisons of high-order nonlinear solvers for the transient Navier–Stokes equations based on homotopy and perturbation techniques

Efficient solvers for the unsteady Navier–Stokes equations are presented. A classic time-stepping scheme is combined with high-order nonlinear solvers coupling homotopy and a perturbation technique. Polynomial and rational representations are used to approximate the unknowns of the problem. A pseudo...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 289; pp. 356 - 370
Main Authors Guevel, Y., Girault, G., Cadou, J.M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2015
Subjects
Computation
Computing time
Homotopy technique
Mathematical analysis
Mathematical models
Navier-Stokes equations
Nonlinear solver
Nonlinearity
Padé approximants
Perturbation method
Perturbation methods
Solvers
Homotopy technique
Perturbation method
Padé approximants
Nonlinear solver
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Summary:Efficient solvers for the unsteady Navier–Stokes equations are presented. A classic time-stepping scheme is combined with high-order nonlinear solvers coupling homotopy and a perturbation technique. Polynomial and rational representations are used to approximate the unknowns of the problem. A pseudo-residual criterion is proposed to improve the efficiency of the solvers. The numerical example considered in this paper is the time-periodic two-dimensional flow around a circular cylinder. Comparisons with the classical first order Newton–Raphson solver are performed. Numerical results reveal that a lower number of matrix factorization is needed with the proposed methods, decreasing the computational effort.
Bibliography:ObjectType-Article-1
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.12.008