Multidomain Extension of a Pseudospectral Algorithm for the Direct Simulation of Wall-Confined Rotating Flows

Abstract

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 academic approaches. Nevertheless, the range of Reynolds numbers reached in industrial devices implies very high resolutions of the spatial problem, which are clearly unreachable using a monodomain approach. Hence, we worked on the multidomain 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 subdomain 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.