Direct numerical simulation of turbulent flows using spectral methods

Direct numerical simulation (DNS) is the most accurate method of solving turbulence in fluids. In DNS the Navier-Stokes equations are solved on a fine mesh to resolve all the spatial and temporal scales present in the flow. In order to ensure high accuracy of the discrete solution, schemes with low numerical errors are necessary. Spectral methods with their low dissipation and dispersion errors are very attractive in this regard. Since their inception in early 1970's, spectral methods have been routinely applied towards direct simulation of turbulent flows. Some of the earliest applications were in isotropic turbulence using Fourier series based methods. As the community turned its attention to solving practical flows, the need for schemes that are efficient in handling complex geometries arose. This led to the development of spectral element methods. In this paper, we describe the application of a semi-structured spectral element method for direct simulation of compressible, wall bounded turbulent flows. A brief outline of the method is first presented. Then we review some of the results for turbulent channel flow and flow over a backward-facing step. The accuracy of the technique is established by comparing our simulation results with experiment and a previous DNS study.