Physics-Informed Minimal Error Simulation Methods for Turbulent Flow Predictions

Simulations of high Reynolds number (Re) separated turbulent flows have faced significant problems for decades as large eddy simulation (LES) is computationally too expensive while Reynolds-averaged Navier-Stokes (RANS) methods and hybrid RANS-LES methods often provide unreliable results. This situation causes serious consequences, we are currently unable to reliably predict very high Re regimes, which hampers applications and our understanding of turbulence structures. The paper reports the advantages of using a strict mathematical approach to derive partially resolving turbulence models. In contrast to popular hybrid RANS-LES, this approach includes a dynamic modification of the turbulence model in response to the actual flow resolution: the model can increase (decrease) its contribution to the simulation in dependence of a low (high) flow resolution. The model is physics-informed via the involvement of information about the resolved motion. Applications of such methods, referred to as continuous eddy simulation (CES), reveal significant advantages, e.g., for the simulation of asymptotic Re regimes. It is worth mentioning that CES methods can be used as resolving LES by avoiding the problem of involving the filter width as artificial length scale, which can become unphysical on coarse grids.