2024/05/04 by Xianglin Shan, Wenbo Cao, Shan, Xianglin +3 · 1 citation
Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2405.02622
openalex publication_date 2024/05/04 · openalex created_date 2024/05/08 · openalex updated_date 2026/07/28
In light of the challenges surrounding convergence and error propagation encountered in Reynolds-averaged Navier-Stokes (RANS) equations with data-driven Reynolds stress closures, researchers commonly attribute these issues to ill-conditioning through conditional number analysis. This paper delves into an additional factor, numerical instability, contributing to these challenges. We conduct global stability analysis for the RANS equations, closed by the Reynolds stress of direct numerical simulation (DNS), with the time-averaged solution of DNS as the base flow. Our findings reveal that, for turbulent channel flow at high Reynolds numbers, significant ill-conditioning exists, yet the system remains stable. Conversely, for separated flow over periodic hills, notable ill-conditioning is absent, but unstable eigenvalues are present, indicating that error propagation arises from the mechanism of numerical instability. Furthermore, the effectiveness of the decomposition method employing eddy viscosity is compared, results show that the spatial distribution and amplitude of eddy viscosity influences the numerical stability.