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-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.