Krylov methods for the incompressible Navier-Stokes equations

Journal Article · Sat Jan 01 04:00:00 EST 1994 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1994.1007· OSTI ID:7106845

Edwards, W S; Tuckerman, L S ^[1]; Friesner, R A ^[2]; Sorensen, D C ^[3]

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1. Univ. of Texas, Austin (United States)
2. Columbia Univ., New York, NY (United States)
3. Rice Univ., Houston, TX (United States)

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 problems. 61 refs., 10 figs., 1 tab.

• OSTI ID: 7106845
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 110:1; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
INCOMPRESSIBLE FLOW
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION