Pressure and time treatment for Chebyshev spectral solution of a Stokes problem
Abstract
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 pseudospectral spacetime 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.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 December 1984
 DOI:
 10.1002/fld.1650041205
 Bibcode:
 1984IJNMF...4.1149D
 Keywords:

 Chebyshev Approximation;
 Computational Fluid Dynamics;
 Incompressible Flow;
 Stokes Law (Fluid Mechanics);
 Flow Velocity;
 Matrices (Mathematics);
 Pressure Effects;
 Time Response;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer