Balancing accuracy and efficiency in the autonomic closure methodology for large eddy simulations

Autonomic closure for large eddy simulations (LES) replaces traditional prescribed subgrid models with an adaptive self-optimizing closure that solves a local, nonlinear, non-parametric system identification problem for each subgrid term, potentially at every point and time in the simulation. This can be regarded as a type of dynamic closure based on highly generalized representations for subgrid terms, each having a large number of degrees of freedom for which coefficients are determined throughout the simulation from corresponding test-scale subgrid terms at a substantial number of nearby reference points. Here we consider autonomic closure for the subgrid stresses, and evaluate numerous implementation choices to examine their effect on the balance between accuracy and efficiency in the autonomic closure methodology. Particular focus is placed on the spatial structure of subgrid production fields and the scale-dependent support-density fields on which large magnitudes of subgrid production are concentrated. We show that a relatively local, second-order, velocity-only, collocated implementation is able to produce subgrid stress and production fields in both isotropic and strongly anisotropic turbulence that closely match the detailed spatial structure and resulting statistics in the exact fields at essentially all resolved scales. This implementation of autonomic closure achieves its accuracy at a computational cost that is O(10³) times lower than previous implementations. The resulting accuracy and efficiency are sufficient to enable autonomic closure to be applied in forward simulations, and we show that an implementation for the subgrid stress identified here integrates stably over long times in a pseudo-spectral LES code without the need for any limiters, added dissipation, or other means of ensuring stability.