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Enhanced algorithms for implementing the spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem
Author(s) -
Ouertani Henda,
Alsaeed Duaa H.,
AlBaity Heyam,
Chorfi Nejmeddine
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5759
Subject(s) - discretization , vorticity , mathematics , cube (algebra) , resolution (logic) , algorithm , boundary (topology) , mathematical analysis , vortex , geometry , computer science , mechanics , physics , artificial intelligence
In this paper, we deal with the numerical resolution of spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem in a square or a cube provided with nonstandard boundary conditions, which involve the normal component of the velocity and the tangential components of the vorticity. Therefore, we propose two algorithms: the Uzawa algorithm and the global resolution. We implemented the two algorithms and compared their results. With global resolution, we obtained a very good accuracy with a small number of iteration.