2021/10/11 by Wybe Rozema, Rozema, Wybe, H. Jane Bae +3 · 1 citation
Earth and Planetary Sciences · Engineering · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Meteorological Phenomena and Simulations
paper · pdf · doi:10.48550/arxiv.2110.05585
openalex publication_date 2021/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a local dynamic model for large-eddy simulation (LES) without averaging in homogeneous directions. It is demonstrated that the widely-used dynamic Smagorinsky model (DSM) has a singular dynamic model constant if it is used without averaging. The singularity can cause exceedingly large local values of the dynamic model constant. If these large values are not mitigated by application of averaging, they can amplify discretization errors and impair the stability of simulations. To improve the local applicability of the DSM, the singularity is removed by replacing the resolved rate-of-strain tensors in the Smagorinsky model with the resolved velocity gradient tensor. These replacements result in the new dynamic gradient Smagorinsky model (DGSM). Results of simulations of three canonical turbulent flows (decaying homogeneous isotropic turbulence, a temporal mixing layer, and turbulent channel flow) are presented to demonstrate the potential of this model. The DGSM provides improved stability compared to the local DSM, and does not require averaging for stability at time step sizes that are typically used for a static locally consistent LES model. Results obtained with the DGSM are generally as accurate as results obtained with the DSM, while the DGSM has lower computational complexity. Moreover, the DGSM is easy to implement and does not require any homogeneous direction in space or time. It is thus anticipated that the model has a high potential for the simulation of complex flows.