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Pressure and time treatment for Chebyshev spectral solution of a Stokes problem
Author(s) -
Deville M.,
Kleiser L.,
MontignyRannou F.
Publication year - 1984
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.1650041205
Subject(s) - mathematics , compressibility , chebyshev polynomials , chebyshev filter , gravitational singularity , space time , mathematical analysis , physics , mechanics , chemical engineering , engineering
To investigate the influences of time scheme, pressure treatment and initial conditions in incompressible fluid dynamics, a Stokes problem is solved numerically on a slab geometry within the framework of spectral approximation in space. Four algorithms are examined: splitting schemes, influence matrix method, penalty formulation and pseudo‐spectral space‐time technique. It is shown that splitting schemes are less accurate than the other processes. Furthermore, the initial field should respect a compatibility condition to avoid singularities at the initial time. If it is not possible to build such a compatible field, the numerical procedure has to present good damping properties at the first steps of the time integration.