Rational Boolean Stabilization of Subgrid Models for Large Eddy Simulations

We develop and demonstrate a new physics-based rational Boolean stabilization method that provides computational stability for any subgrid stress model in large eddy simulations, while producing far smaller changes in the originally unstable stress and production fields than do current ad hoc stabilization methods. A pseudo-spectral code having numerics that are shown here to be almost entirely non-dissipative yet stable is used to conduct simulations with unstable subgrid stress models. Results show that initial instability, subsequent unbounded growth, and eventual machine overflow are due to a highly localized dynamical process involving interactions among terms in the kinetic energy transport equation. This process begins first at one material point and then over time at increasingly more material points, with the local growth rate of kinetic energy being the same for all unstable material points, and with overflow typically occurring at the material point where this process began first. A Lagrangian backtracking scheme is developed and applied to enable backward-in-time tracking of all terms in the kinetic energy transport equation for any unstable material point. This gives insights into the dynamics that produce this local instability and its subsequent unbounded growth, with the initial instability resulting from interactions between the subgrid production and subgrid redistribution terms. From this we develop a rational Boolean stabilization method, which uses the local subgrid production and subgrid redistribution rates to determine where and how individual components of the subgrid stress should be rescaled to provide local backwardtransfer reduction or forward-transfer amplification. This stabilizes all subgrid stress models while producing only small changes in their original subgrid stress and production fields. Rational Boolean stabilization is computationally fast, and can be generalized to stabilize models for other subgrid terms while producing only small changes in their originally unstable fields. This solves a key problem that has previously limited the accuracy of large eddy simulations.