Space-time mesh adaptation for the VMS-Smagorinsky modeling of high Reynolds number flows

• The space-time adaptive procedure has proven effective in significantly improving computational efficiency across various flow regimes. • Anisotropic meshes effectively capture flow singularities and near-wall behavior with a limited number of mesh elements, and eliminate the need for wall law corrections. • The adaptive time-step strategy maintains small time-steps during rapid flow changes for accurate resolution, while allowing larger steps in steady-state conditions to reduce computational costs. • Numerical tests on complex flow configurations, such as lid-driven cavity and backward-facing step cases, are in agreement with reference solutions in the literature and confirm the method’s ability to capture critical flow features with reduced computational effort. Traditional methods, such as Reynolds-Averaged Navier-Stokes (RANS) equations and Large Eddy Simulations (LES), provide consolidated tools for the numerical approximation of high Reynolds number flows in a wide range of applications - from green energy to industrial design. In general, RANS modeling is practical when the main interest is the time-averaged flow behavior. LES equations offer detailed insights into flow dynamics and a more accurate solution, but the high computational demand necessitates innovative strategies to reduce costs while maintaining precision. In this study, we enhance the Variational MultiScale (VMS)-Smagorinsky LES model by relying on an adaptive discretization strategy in both space and time, driven by a recovery-based a posteriori error analysis. We assess the effectiveness of the approach in capturing flow characteristics across a wide range of Reynolds numbers through benchmark tests.