Spectral 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

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