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2012.16: Unstructured finite element method for the solution of the Boussinesq problem in 3D

2012.16: Christopher A. Smethurst, David J. Silvester and Milan D. Mihajlovic (2012) Unstructured finite element method for the solution of the Boussinesq problem in 3D.

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Abstract

We present a numerical method for the monolithic discretisation of the Boussinesq system in three spatial dimensions. The key ingredients of the proposed methodology are the finite element discretisation of the spatial part of the problem using unstructured tetrahedral meshes, an implicit time integrator, based on adaptive predictor-corrector scheme (the explicit AB2 method with the implicit stabilised trapezoid rule), and a new preconditioned Krylov subspace solver for the rersulting linearised discrete problem. We test the proposed methodology on a number of physically relevant cases, including laterally heated cavities and the Rayleigh-B\'enard convection, and compare the obtained results with other numerical methods and the experiments.

Item Type:MIMS Preprint
Uncontrolled Keywords:Boussinesq, unstructured finite elements, adaptive timestepping, Krylov solvers, block preconditioning, algebraic multigrid.
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MSC 2000 > 76 Fluid mechanics
MIMS number:2012.16
Deposited By:Dr Milan Mihajlovic
Deposited On:18 January 2012

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