An Efficient Data-Driven Closure Modeling Framework for Interpretable Sub-Grid Scale Stress Model Development Via Sparse Regression

Despite the projected advancements in computer speed and memory in the coming decades, high-fidelity, complex turbulent flow field simulations are fated intractable on average computers for the foreseeable future. This indicates the pressing need for new methodologies to build accurate turbulence closure models that use fewer computational resources. In recent years, data-driven approaches -- most popularly, neural networks -- have demonstrated promise for advancing the state-of-the-art in terms of predictive performance. Neural networks, however, suffer from a lack of interpretability due to their “black box” nature, which inevitably obscures the underlying physics and routinely increases the computational cost over that of conventional models. To address these issues, we propose a data-driven framework to discover explicit, algebraic, closed-form nonlinear eddy viscosity (NLEV) models of the sub-grid scale (SGS) stress tensor via sparse regression techniques. To embed invariance properties directly into the model form, training is performed over a minimal tensor basis that is scaled by a truncated infinite polynomial expansion of invariant scalars. We modulate model dissipation error by implementing a custom optimization function. Our SGS modeling framework also generalizes to anisotropic grids by using a mapping to the isotropic space. We demonstrate the robustness and efficiency of our NLEV model in both a priori and a posteriori tests.