On the generation of synthetic divergence-free homogeneous anisotropic turbulence

It is well known that the generation of appropriate unsteady boundary conditions represents an important component of successful Large Eddy Simulations in turbulent flows. In particular, when Computational Wind Engineering applications are considered, a recurrent problem consists in imposing turbulent fluctuations characterized by given spectra and length scales at the inlet boundary. In the present contribution, firstly, currently available techniques for the generation of synthetic turbulence are revised with a focus on their mathematical formulation. Then, two new approaches for the generation of homogeneous turbulence are proposed. The first one can be seen as a correction over existing techniques which allows to control the obtained length scales. The second method, conceived to generate anisotropic turbulence characterized by arbitrary harmonic content in both time and space, is designed to be computationally efficient, to guarantee the divergence-free condition and to ensure a good approximation of the resulting turbulence integral scales. Finally, the procedure is validated by synthesizing a homogeneous turbulent field characterized by time and length scales typical of the atmospheric boundary layer showing good results.