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

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

Discrete and Continuous Dynamical Systems - Series S (DCDS-S). 2012;5(6):1195-1221.

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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.

Bibliographic metadata

Type of resource:
Content type:
Publication type:
Published date:
Volume:
5
Issue:
6
Start page:
1195
End page:
1221
Pagination:
27
Digital Object Identifier:
10.3934/dcdss.2012.5.1195
Access state:
Active

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:172639
Created by:
Silvester, David
Created:
2nd October, 2012, 16:19:55
Last modified by:
Silvester, David
Last modified:
11th March, 2014, 21:19:56