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2011.104: A framework for the development of implicit solvers for incompressible flow problems

2011.104: David Silvester, Alexei Bespalov and Catherine E. Powell (2011) A framework for the development of implicit solvers for incompressible flow problems.

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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.

Item Type:MIMS Preprint
Uncontrolled Keywords:Navier-Stokes, Boussinesq, finite element approximation, stochastic Galerkin approximation, implicit time stepping, preconditioning, algebraic multigrid.
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MSC 2000 > 76 Fluid mechanics
MIMS number:2011.104
Deposited By:professor david silvester
Deposited On:05 December 2011

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