Enhanced algorithms for implementing the spectral discretization of the vorticity-velocity-pressure formulation of Stokes problem

摘要

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.