Assessment of different cut-off (filter-width) prescription approaches for the scale-resolving PANS method

The Partially-Averaged Navier-Stokes (PANS) is a scale-resolving turbulence computational approach designed to resolve large scale fluctuations and model the remainder with appropriate closures. Depending upon the prescribed cut-off length (filter width) the method adjusts seamlessly from the Reynolds-Averaged Navier-Stokes (RANS) to the Direct Numerical Solution (DNS) of the Navier-Stokes equations. The unresolved to total kinetic energy ratio f_k is the cut-off control parameter and its specification requires the knowledge of the local turbulent (resolved + unresolved) kinetic energy. While the unresolved kinetic energy is computed directly from model equations, in most current formulations, the resolved kinetic energy is obtained by suitably averaging the resolved field – as in dynamic Smagorinsky LES computations. As the averaging process is expensive, recently alternate specification approaches have been developed. One such approach is to solve an additional equation for resolved turbulent kinetic energy as first proposed by Basara and Girimaji (2013) and further developed by Basara, Pavlovic and Girimaji (2018). In this presentation, we analyse the various f_k-specification approaches. Important conclusions regarding the merits of each method are drawn.