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Silvester, David; Elman, Howard; Kay, David; Wathen, Andrew

Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. (English) Zbl 0983.76051

J. Comput. Appl. Math. 128, No. 1-2, 261-279 (2001).
Summary: We outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of Navier-Stokes equations. We describe a very general strategy for preconditioning that has two basic building blocks; a multigrid V-cycle the scalar convection-diffusion operator, and a multigrid V-cycle for pressure Poisson operator. We present numerical experiments illustrating that a simple implementation of our approach leads to effective and robust solver strategy, in that the convergence rate is independent of the grid, robust with respect to the time-step, and only deteriorates very slowly as the Reynolds number is increased.

Cited in 4 Reviews
Cited in 67 Documents

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs

Keywords:

linearized Navier-Stokes equations; incompressible flow; multigrid iteration; operator splitting; preconditioning; multigrid V-cycle; scalar convection-diffusion operator; pressure Poisson operator; convergence rate

Software:

CGS
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\textit{D. Silvester} et al., J. Comput. Appl. Math. 128, No. 1--2, 261--279 (2001; Zbl 0983.76051)
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References:

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