A Generalized Method for External Forcing of DNS of Complex, Unsteady, and Anisotropic Turbulent Flows

Direct numerical simulations (DNS) of statistically stationary, homogeneous, isotropic turbulence have historically served as one of the primary tools for theoretical studies of turbulence. To sustain such flows, a variety of external forcing approaches have been suggested, which intend to represent the action of larger energetic flow scales not captured in the DNS. The key limitation of the prior strategies is that the effect of larger scales is condensed into a single scalar parameter - rate of kinetic energy injection, which decouples DNS from any realistic external flow features. Here we propose a generalized method for forcing fully resolved simulations of complex turbulent flows, which can be highly unsteady (non-equilibrium), anisotropic, and inhomogeneous. Large-scale flow structure is extracted from an appropriately filtered field from a large eddy simulation (LES) and is then used to force a fully resolved simulation of a particular flow subregion. This approach is implemented in physical space in contrast to prior spectral nudging strategies. The approach allows one to capture the details of a specific region of interest, which cannot be otherwise resolved in lower-fidelity LES. A detailed a priori and a posteriori analysis of the method performance is presented.