Abstract
This survey paper reviews some recent developments in the design of robust solution methods for the NavierStokes 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 AdamsBashforth 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.
Original language  English 

Pages (fromto)  11951221 
Number of pages  26 
Journal  Discrete and Continuous Dynamical Systems. Series S 
Volume  5 
Issue number  6 
DOIs  
Publication status  Published  Dec 2012 
Keywords
 Algebraic multigrid
 Boussinesq
 Finite element approximation
 Implicit time stepping
 NavierStokes
 Preconditioning
 Stochastic Galerkin approximation
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