A framework for the development of  implicit solvers for incompressible flow problems

David J. Silvester; Alex Bespalov; Catherine E. Powell

doi:10.3934/dcdss.2012.5.1195

Article Contents

2012, Volume 5, Issue 6: 1195-1221. Doi: 10.3934/dcdss.2012.5.1195 open access

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A framework for the development of implicit solvers for incompressible flow problems

1.
School of Mathematics, The University of Manchester, Manchester M13 9PL

Received: November 30, 2011

Revised: February 29, 2012

Published: November 2012

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Abstract

This survey paper reviews some recent developments in the design of robust solution methods for the Navier--Stokes equations modelling incompressible fluid flow. There are two building blocks in our solution strategy. First, an implicit time integrator that uses a stabilized trapezoid rule with an explicit Adams--Bashforth method for error control, and second, a robust Krylov subspace solver for the spatially discretized system. Numerical experiments are presented that illustrate the effectiveness of our generic approach. It is further shown that the basic solution strategy can be readily extended to more complicated models, including unsteady flow problems with coupled physics and steady flow problems that are nondeterministic in the sense that they have uncertain input data.

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Mathematics Subject Classification: Primary: 65M22, 76D05, 76D05; Secondary: 76M10.

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