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Presure and time treatment for Chebyshev spectral solution of a Stokes problem. (English) Zbl 0554.76033
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.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
76M99 Basic methods in fluid mechanics
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