In this work, we improve an existing pseudospectral algorithm, in order to extend its properties to a multidomain patching of a rotating cavity. Viscous rotating flows have been widely studied over the last decades, either on industrial or aca-demic approaches. Nevertheless, the range of Reynolds numbers reached in indus-trial devices implies very high resolutions of the spatial problem, which are clearly unreachable using a monodomain approach. Hence, we worked on the multido-main extension of the existing divergence-free Navier-Stokes solver with a Schur approach. The particularity of such an approach is that it does not require any sub-domain superposition: the value of a variable on the boundary between two adjacent subdomains is treated as a boundary condition of a local Helmholtz solver. This value is computed on a direct way via a so-called continuity influence matrix and the derivative jump of an homogeneous solution computed independently on each subdomain. Such a method is known to have both good scalability and accuracy. It has been validated on two well documented three-dimensional rotating flows.