Edwards, W. S.; Tuckerman, L. S.; Friesner, R. A.; Sorensen, Danny C. Krylov methods for the incompressible Navier-Stokes equations. (English) Zbl 0792.76062 J. Comput. Phys. 110, No. 1, 82-102 (1994). Summary: Methods are presented for time evolution, steady-state solving and linear stability analysis for the incompressible Navier-Stokes equations at low to moderate Reynolds numbers. The methods use Krylov subspaces constructed by the Arnoldi process from actions of the explicit Navier- Stokes right-hand side and of its Jacobian, without inversion of the viscous operator. Time evolution is performed by a nonlinear extension of the method of exponential propagation. Steady states are calculated by inexact Krylov-Newton iteration using ORTHORES and GMRES. Linear stability analysis is carried out using an implicitly restarted Arnoldi process with implicit polynomial filters. A detailed implementation is described for a pseudospectral calculation of the stability of Taylor vortices with respect to wavy vortices in the Couette-Taylor problem. Cited in 1 ReviewCited in 76 Documents MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76D05 Navier-Stokes equations for incompressible viscous fluids 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs Keywords:linear stability analysis; Krylov subspaces; Arnoldi process; method of exponential propagation; Krylov-Newton iteration; ORTHORES; GMRES; pseudospectral calculation; Taylor vortices; Couette-Taylor problem PDFBibTeX XMLCite \textit{W. S. Edwards} et al., J. Comput. Phys. 110, No. 1, 82--102 (1994; Zbl 0792.76062) Full Text: DOI Link