Preconditioned spectral multi-domain discretization of the incompressible Navier–Stokes equations

In this paper we present a preconditioned multi-domain algorithm applied to the elliptic kernels arising from the spectral collocation of the incompressible Navier–Stokes equations in three space dimensions with one homogeneous direction. The technique, based on the iterative solution of the Schur complement matrix, allows for efficient numerical solution of the operators in complex geometries consisting of a collection of non-overlapping rectangular subdomains. The method is shown to be nearly optimal in terms of condition number behavior in a double path of refinement strategy, i.e. whenever both the number of Legendre modes and the number of subdomains are significantly increased. It is thus well suited for engineering applications in the fields of direct numerical simulation and large eddy simulation of turbulence.