Missing large scales: Development and implementation of a physics-based turbulence forcing scheme for numerical simulations of compressible flows

When performing direct numerical simulations of highly-turbulent flows, it is often prohibitively expensive to simulate complete flow geometries. A well-selected portion of the domain is then chosen. However, by doing so one usually misses Turbulent Kinetic Energy (TKE) injection due to shear by the large scales. There are many techniques available in the literature to inject TKE, however none of these follow directly from the Navier-Stokes equations. This is the goal of the present work. We decompose the velocity field into small-scale and large-scale components. The latter is assumed to be known beforehand, and we solve for the small-scale component only. We have already applied this strategy to incompressible flows, but not to compressible ones, where special care must be taken regarding the energy equation. Implementation of this scheme in the finite-difference solver NGA is discussed and preliminary results are presented. In particular, we investigate the impact of periodic boundary conditions, which can cause some dilatational velocity modes to grow boundlessly.