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Krylov methods for the incompressible Navier-Stokes equations. (English) Zbl 0792.76062

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.

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
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