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Stability of convective flows in cavities: solution of benchmark problems by a low‐order finite volume method
Author(s) -
Gelfgat Alexander Yu.
Publication year - 2006
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.1291
Subject(s) - krylov subspace , finite volume method , solver , mathematics , richardson extrapolation , convergence (economics) , benchmark (surveying) , generalized minimal residual method , jacobian matrix and determinant , extrapolation , preconditioner , stability (learning theory) , dimension (graph theory) , mathematical optimization , computer science , iterative method , mathematical analysis , physics , mechanics , geodesy , machine learning , geography , pure mathematics , economics , economic growth
A problem of stability of steady convective flows in rectangular cavities is revisited and studied by a second‐order finite volume method. The study is motivated by further applications of the finite volume‐based stability solver to more complicated applied problems, which needs an estimate of convergence of critical parameters. It is shown that for low‐order methods the quantitatively correct stability results for the problems considered can be obtained only on grids having more than 100 nodes in the shortest direction, and that the results of calculations using uniform grids can be significantly improved by the Richardson's extrapolation. It is shown also that grid stretching can significantly improve the convergence, however sometimes can lead to its slowdown. It is argued that due to the sparseness of the Jacobian matrix and its large dimension it can be effective to combine Arnoldi iteration with direct sparse solvers instead of traditional Krylov‐subspace‐based iteration techniques. The same replacement in the Newton steady‐state solver also yields a robust numerical process, however, it cannot be as effective as modern preconditioned Krylov‐subspace‐based iterative solvers. Copyright © 2006 John Wiley & Sons, Ltd.