Bridging turbulent scales: A unified LES approach from low to high Reynolds numbers using TSDIA and GOY Shell models

Large Eddy Simulation (LES) has become a widely adopted method for modeling turbulence across various fields, such as aerospace, wind energy, and urban wind flow analysis. While traditional LES models are highly effective at high Reynolds numbers, they face challenges at low Reynolds numbers due to the absence of a clearly defined inertial subrange. This paper introduces an improved LES approach by integrating Yoshizawa's Two-Scale Direct Interaction Approximation (TSDIA) theory and the GOY shell model. This combined method extends the applicability of LES by capturing turbulence features across both inertial and dissipation ranges, overcoming limitations found in conventional models. By deriving model constants directly from the shell model, this approach avoids reliance on empirical values and enhances accuracy, particularly at low Reynolds numbers. Validation against DNS data demonstrates a significant improvement in prediction accuracy, offering a more comprehensive and adaptable solution for turbulent flow simulations across a wide range of practical applications. This method provides a more robust foundation for industrial fluid simulations and environmental modeling.