2006.376: Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow

2006.376: David Silvester, Howard Elman, David Kay and Andrew Wathen (2001) Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. Journal of Computational and Applied Mathematics, 128 (1-2). pp. 261-279. ISSN 0377-0427

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DOI: 10.1016/S0377-0427(00)00515-X

Abstract

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 for the scalar convection–diffusion operator, and a multigrid V-cycle for a pressure Poisson operator. We present numerical experiments illustrating that a simple implementation of our approach leads to an 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.

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