Adaptive Scale-Similar Closure of the Subgrid Stress and Subgrid Scalar Flux in Large Eddy Simulations

We demonstrate an adaptive scale-similar closure approach that represents subgrid terms accurately and stably even at the smallest resolved scales of a simulation. This is based on scale similarity and generalized representations of subgrid terms from the complete and minimal tensor representation theory of Smith (1971). Tensor polynomial coefficients adapt to the local turbulence state via system identification at a test-filter scale. The local test-scale coefficients are rescaled to the LES-scale to evaluate the subgrid term. Resulting stress and production fields, and scalar flux and scalar dissipation fields, are nearly identical to corresponding true fields. Even in a low-dissipation pseudo-spectral code, this closure is stable without any added dissipation, and with only minor added dissipation shows E(k) ~ k-5/3 scaling to the smallest resolved scales. A posteriori tests show greatly improved accuracy in inner-scale statistics compared to traditional closure with a prescribed subgrid model. When accuracy is needed even at the smallest resolved scales, the 3X longer run-time compared to traditional closure with the dynamic Smagorinsky model may be acceptable, and this new closure approach can provide stable and accurate simulations across all resolved scales.