Solution of the Navier-Stokes equations by a spectral method of subdomains

A numerical method for solution of the Navier-Stokes equations for unsteady, incompressible viscous flows over complex geometries is presented. The technique involves definition of two subdomain ensembles. The subdomains have a curved, two-dimensional geometry, and overlap. Calculations are carried out to solve for the pressure, the pressure fluctuations, and the Poisson problem. A spectral method is used in the solution of the Poisson problem, with a finite difference scheme being imposed on the reference domain before the division into subdomains. Limiting conditions are imposed on the internal and external boundaries. An example is provided in the form of a flow through a channel with a backward facing step. The results are in accord with those obtained with the finite element method, and were obtained with a faster convergence.