Krylov Methods for the Incompressible Navier-Stokes Equations
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 s...
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| Veröffentlicht in: | Journal of computational physics 1994, Vol.110 (1), p.82-102 |
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| container_end_page | 102 |
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| container_issue | 1 |
| container_start_page | 82 |
| container_title | Journal of computational physics |
| container_volume | 110 |
| creator | Edwards, W.S. Tuckerman, L.S. Friesner, R.A. Sorensen, D.C. |
| description | 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. |
| doi_str_mv | 10.1006/jcph.1994.1007 |
| format | Article |
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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. 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| ispartof | Journal of computational physics, 1994, Vol.110 (1), p.82-102 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | 990200 -- Mathematics & Computers Classical and quantum physics: mechanics and fields Classical mechanics of continuous media: general mathematical aspects Computational methods in fluid dynamics COMPUTERIZED SIMULATION DIFFERENTIAL EQUATIONS ENGINEERING EQUATIONS Exact sciences and technology FLUID FLOW Fluid mechanics: general mathematical aspects GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE INCOMPRESSIBLE FLOW NAVIER-STOKES EQUATIONS NUMERICAL SOLUTION PARTIAL DIFFERENTIAL EQUATIONS Physics SIMULATION 420400 -- Engineering-- Heat Transfer & Fluid Flow |
| title | Krylov Methods for the Incompressible Navier-Stokes Equations |
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