Adaptive Scale-Similar Closure for Large Eddy Simulations. Part 2: Subgrid Scalar Flux Closure

We extend and demonstrate the adaptive scale-similar closure approach from Part 1 to the subgrid scalar flux (formula presented) to enable accurate and stable large eddy simulations of scalar fields (formula presented) even at or near the smallest resolved scales. This closure approach is based on scale similarity and generalized representation of the subgrid scalar flux vector via the complete and minimal tensor representation theory of Smith (1971). The coefficients in the generalized representation are adapted to the local turbulence state by solving a local system identification problem at a test-filter scale. The resulting test-scale coefficients are rescaled to the LES-scale and used in the generalized representation to evaluate the local subgrid scalar flux. Resulting (formula presented) fields and scalar energy subgrid production fields (formula presented) are seen in a priori tests to be substantially more accurate than corresponding results from traditional prescribed-model closures. Even when implemented in a low-dissipation pseudo-spectral code, this adaptive scalesimilar closure for the subgrid scalar flux is stable with substantially less added dissipation than is needed for traditional prescribed-model closures. Results from a posteriori tests in which this adaptive scale-similar closure approach is used for both the subgrid scalar flux (formula presented) and the subgrid stress (formula presented) show greatly improved accuracy in scalar statistics compared to traditional closure with prescribed subgrid models. In LES where high accuracy is needed even at or near the smallest resolved scales, the slightly longer simulation time needed when evaluating the subgrid stress and subgrid scalar flux via adaptive scale-similar closure may be acceptable to gain the improved accuracy it provides across all scales.