Autonomic subgrid-scale closure for large eddy simulations

Motivated by advances in constrained optimization methods, a fundamentally new autonomic closure for LES is presented that invokes a self-optimization method for the subgrid-scale stresses instead of a predefined turbulence model. This autonomic closure uses the most general dimensionally-consistent expression for the local subgrid-scale stresses in terms of all resolved-scale variables and their products at all spatial locations and times, thereby also incorporating all possible gradients of all resolved variables and products. In so doing, the approach addresses all possible nonlinear, nonlocal, and nonequilibrium turbulence effects without requiring any direct specification of a subgrid-scale model. Instead it uses an optimization procedure with a test filter to find the best local relation between subgrid stresses and resolved-scale variables at every point and time. We describe this autonomic closure approach, discuss truncation, regularization, and sampling in the optimization procedure, and present results from a priori tests using DNS data for homogeneous isotropic and sheared turbulence. Even for the simplest 2^nd-order truncation of the general formulation, substantial improvements over the dynamic Smagorinsky model are obtained with this new autonomic approach to turbulence closure.