A New Autonomic Closure for Large Eddy Simulations

We present a fundamentally new autonomic subgridscale closure for large eddy simulations (LES) that solves a nonlinear, nonparametric system identification problem instead of using a predefined turbulence model. The autonomic approach expresses the local SGS stress tensor as the most general unknown nonlinear function of the resolvedscale primitive variables at all locations and times using a Volterra series. This series is analogous to a Taylor series expansion in both time and space, and incorporates nonlinear, nonlocal, and nonequilibrium turbulence effects. The series introduces a large number of convolution kernel coefficients that are found by solving an inverse problem to minimize the error in representing known subgrid-scale stresses at a test filter scale. The optimized coefficients are then projected to the LES scale by invoking scale similarity in the inertial range and applying appropriate renormalizations. This new closure approach avoids the need to specify a turbulent constitutive model and instead identifies an optimal model on the fly. Here we present the most general formulation of the new autonomic approach and outline an inverse modeling method for optimizing the coefficients. We then explore truncations of the series expansion and demonstrate the effects of regularization and sampling on the optimal coefficients. Finally, we perform a priori tests of this approach using data from direct numerical simulations of homogeneous isotropic and sheared turbulence. We find substantial improvements over the Dynamic Smagorinsky model, even for a 2nd order time-local truncation of the present closure.