Anisotropic mesh adaptation techniques for the Variational MultiScale-Smagorinsky modeling of high Reynolds flows
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The numerical approximation of turbulent phenomena in fluid dynamics is commonly demanded in several application fields, such as green energy technologies, medical diagnostics and industrial design. With this regard, the literature proposes cutting-edge models and methods in order to account for the accurate description of turbulent flows, including the inherent multiscale and time-dependent features, at an affordable simulation cost. Among the turbulence models available in the literature, we focus on the Variational MultiScale (VMS)-Smagorinsky model presented in [1]. This approach introduces an artificial viscosity only at a local level, specifically in the portions of the domain where turbulent phenomena are relevant, thus avoiding the global overdiffusive effect that characterizes the classical Smagorinsky model. In this setting, we propose to enrich the VMS-Smagorinsky approach with an anisotropic mesh adaptation procedure, with the goal of following the intrinsic directionalities of the flow by tailoring the shape, the size and the orientation of the mesh. Specifically, drawing inspiration from the standard Zienkiewicz-Zhu error estimator and its anisotropic variants, we opt to drive the grid adaptation procedure based on the gradient of one or more variables that are relevant in the turbulent regime and concurrently vary across the domain. In this presentation, we introduce the proposed adaptive method and we apply it to several benchmark cases for testing. In particular, we explore the impact of the variables guiding the mesh adaptation procedure on numerical modeling. The options considered include fluid velocity, pressure and wall functions. Morever, we compare the proposed method with established approaches, including global mesh refinement, isotropic grid adaptation, and wall correction schemes, assessing both computational performance and solution accuracy. REFERENCES [1] T. Chacon Rebollo, R. Lewandowski. Mathematical and Numerical Foundations of Turbulence Models and Applications. Birkhäuser/Springer, New York (2014). [2] S. Micheletti, S. Perotto. Anisotropic adaptation via a Zienkiewicz–Zhu error estimator for 2d elliptic problems. Numerical mathematics and advanced applications 2009: proceedings of Enumath 2009, the 8th European conference on numerical mathematics and advanced applications (2010) 645-653.