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Unstructured finite element method for the solution of the Boussinesq problem in three dimensions
Author(s) -
Smethurst C.A.,
Silvester D.J.,
Mihajlović M.D.
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3823
Subject(s) - discretization , solver , polygon mesh , finite element method , mathematics , krylov subspace , integrator , tetrahedron , subspace topology , mesh generation , mathematical analysis , computer science , mathematical optimization , linear system , geometry , engineering , structural engineering , computer network , bandwidth (computing)
SUMMARY 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 second‐order Adams–Bashforth method with the implicit stabilised trapezoid rule), and a new preconditioned Krylov subspace solver for the resulting linearised discrete problem. We test the proposed methodology on a number of physically relevant cases, including laterally heated cavities and the Rayleigh–Bénard convection. Copyright © 2013 John Wiley & Sons, Ltd.