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

Y. Guevel ^[1] ; G. Girault ^[1] ; J.M. Cadou ^[1]
1. [1] Université de Bretagne Sud, France
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 356-370
Idioma: inglés
DOI: 10.1016/j.cam.2014.12.008
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Resumen
- 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.