A Divergence-Free Multidomain Spectral Solver of the Navier-Stokes Equations in Geometries of High Aspect Ratio

In order to solve with high accuracy the incompressible Navier-Stokes equations in geometries of high aspect ratio, one has developed a spectral multidomain algorithm, well adapted to the parallel computing. In cases of 2D problems, a Chebyshev collocation method and an extended influence matrix-technique are used in each subdomain, to solve the generalized Stokes problem which results from the discretization in time. The continuity conditions, needed at the interfaces of each subdomain, are computed by using again an influence matrix, the setup of which ensures all the necessary compatibility conditions, especially the incompressibility. This work is also described for 3D problems with one homogeneous direction. A study of accuracy versus the number of subdomains is presented, as well as an example of an application concerned with Rayleigh-Bénard convection in a cavity of large aspect ratio.