Silvester, David and Bespalov, Alexei and Powell, Catherine E. (2011) A framework for the development of implicit solvers for incompressible flow problems. [MIMS Preprint]
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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 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics |
| Depositing User: | professor david silvester |
| Date Deposited: | 05 Dec 2011 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1724 |
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