Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic nature of the model is that the Subgrid-Scale (SGS) kinetic energy production and dissipation are in balance, i.e., P/ε = 1. In this work, we propose an improved EASSM design that does not involve this precalibration and retains the ratio P/ε as a space and time dependent variable. Our model is based on the partial differential evolution equation for the SGS kinetic energy ksgs and the assumption that the ratio P/ε evolves slower in time than ksgs. Computational results for simple cases of forced isotropic turbulence show that the new model is able to track the evolution of the SGS kinetic energy significantly better than the dynamic and non-dynamic EASSMs of Marstorp et al. (2009). Also the predicted kinetic energy spectra and resolved dissipation evolution are in excellent agreement with reference data from Direct Numerical Simulations (DNS).

We investigate the underlying assumptions of Explicit Algebraic Subgrid-Scale Models (EASSMs) for Large-Eddy Simulations (LESs) through an a priori analysis using data from Direct Numerical Simulations (DNSs) of homogeneous isotropic and homogeneous rotating turbulence. We focus on the performance of three models: the dynamic Smagorinsky (DSM) and the standard and dynamic explicit algebraic models as in Marstorp et al. (2009), here refereed to as SEA and DEA. By comparing correlation coefficients, we show that the subgrid scale (SGS) stress tensor is better captured by the EA models. Overall, the DEA leads to the best performance, which is evidenced by comparing how each model reproduces the probability density function (p.d.f.) of the SGS kinetic energy production. Next, we evaluate the approximations that are inherent to EA models such as the model for the pressure-strain correlation. We analyze the performance of three pressure-strain models commonly employed in the RANS framework: the LRR-QI, the LRR-IP, and the SSG models. Again, through correlation coefficients, and by splitting the pressure contributions into slow and rapid, we assess the relative performance of each model. Finally, we test the local equilibrium assumption of Marstorp et al. (2009), which considers a local balance between the SGS kinetic energy production and the dissipation. The probability density function shows that the ratio of SGS kinetic energy production to dissipation is distributed over a broad range of values and that the local equilibrium assumption can be only viewed as a mathematical simplification.