Spectra Element-Fourier Method for Transitional Flows in Complex Geometries

An efficient spectral element-Fourier method is presented for the direct numerical simulation of transitional internal flows in complex geometries. This method is applied for the spatial discretization of the unsteady, incompressible, three-dimensional Navier-Stokes equations in the velocity-pressure formulation. The resulting discrete equations are solved by a semi-implicit method in time, where the nonlinear convective term is treated explicitly. Direct numerical simulations are performed to investigate the spatial structure and temporal evolution of two- and three-dimensional transitional flows in grooved channels