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A Petrov–Galerkin method for flows in cavities: enclosure of aspect ratio 8
Author(s) -
Suslov Sergey A.,
Paolucci Samuel
Publication year - 2002
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.386
Subject(s) - enclosure , galerkin method , petrov–galerkin method , ordinary differential equation , mathematics , boundary value problem , flow (mathematics) , aspect ratio (aeronautics) , computation , basis (linear algebra) , mathematical analysis , finite element method , differential equation , geometry , physics , computer science , algorithm , telecommunications , optoelectronics , thermodynamics
A Petrov–Galerkin method for computations of fully enclosed flows is developed. It makes use of divergence‐free basis functions which also satisfy the boundary conditions for the velocity field. This allows the elimination of the unknown pressure. The computational procedure reduces to the solution of a system of non‐linear first‐order ordinary differential equations for the spectral expansion coefficients. We illustrate the effectiveness and accuracy of the method by solving the problem of the two‐dimensional thermoconvective flow in a rectangular cavity of aspect ratio 8 at Rayleigh number 3.4×10 5 . Copyright © 2002 John Wiley & Sons, Ltd.