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

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
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