Application of the spectral multidomain method to the Navier-Stokes equations

An application of the spectral multidomain method to the two-dimensional, time-dependent, incompressible Navier-Stokes equations is presented. The governing equations are discretized on a non-staggered, stretched mesh with a mixed finite difference/Chebyshev method and are integrated by a time-splitting procedure. The accuracy of the multidomain method is demonstrated for two different channel flow configurations, one with a backward-facing step and the other with a rectangular step. The method is then applied to the investigation of the effects of an isolated, two-dimensional roughness element on the spatial development of instability waves in boundary layers.