A variational multiscale method for turbulent flow simulation with adaptive large scale space

In turbulent flows it is only feasible to simulate large flow structures. Variational multiscale (VMS) methods define these flow structures by projections onto appropriate function spaces. This paper presents a finite element VMS method which chooses the large scale projection space adaptively. The adaption controls the influence of an eddy viscosity model and it is based on the size of the so-called resolved small scales. The adaptive procedure is described in detail. Numerical studies at a turbulent channel flow and a turbulent flow around a cylinder are presented. It is shown that the method selects the large scale space in a reasonable way and that appropriately chosen parameters improve the results compared to the basic method, which uses the same local large scale space in the whole domain and for all times.