Secondment from Politecnico di Milano to Virtualmech

E. Temellini (Politecnico di Milano) had a 3 month (February – May 2023) secondment at Virtualmech on the topic of Model reduction and mesh adaptation techniques for VMS – Smagorinsky turbulence model.

Turbulence is a phenomenon encountered in the modeling of several engineering applications (e.g., solar panels and wind turbines). The high complexity of turbulent problems from a modeling viewpoint is followed by a huge computational effort, with a view to guaranteeing a reliable discrete approximation. According to the goals in WP2, final goal of this research is the development of reliable and computationally efficient mathematical tools for the modeling of turbulent flows in pipes, with a strong interest for applications in hemodynamics and renewable energy technologies. The activity carried out during the months spent at VirtualMech for the secondment, can be thus itemized:

– Performed an extensive literature review on turbulence models, with a particular interest for Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) techniques. Due to specific modeling requirements as well as to the availability of in-house implemented codes, we have gone for LES approaches, with a particular focus on the Smagorinsky’s model (SM), and the Variational Multiscale (VMS) methodology applied to the Smagorinsky’s model (VMS-SM);

– Being familiarized with a 2D VMS-SM code implemented in FreeFEM, provided by Professor Tomas Chacon Rebollo, where the standard finite element solver is enriched by an isotropic mesh adaptation procedure driven by a residual-based error estimator. In particular, the code has been revised to match with the specific WP2’s research goals. Mesh adaptation can be conceived a first mathematical tool to contain the computational cost characterizing the simulation of turbulent flows, with the possibility of resorting to a very fine mesh only in correspondence with the regions characterized by strong turbulent effects;

– Successively explored the possibility to resort to an anisotropic mesh adaptation technique to discretize LES-VMS-SM models, with the aim of further enhance the computational benefits led by an isotropic adapted grid. As a matter of fact, by properly tuning the shape, the size and the orientation of mesh elements, anisotropic meshes guarantee a certain solution accuracy with a considerably lower number of elements, when compared with uniformly refined and isotropic adapted grids. To drive the anisotropic mesh adaptation, I have exploited the anisotropic variant of the well-known Zienkiewicz- Zhu (ZZ) error estimator, which has already been successfully applied to many interdisciplinary problems, such as Zienkiewicz- Zhu error estimator is used to control the gradient of a certain quantity of interest. So far, I have selected the two components of the flow velocity and the flow pressure as driving quantity, in a single as well as in a combined approach. The analysis is currently limited to stationary 2D flows characterized by a moderate Reynolds number, with the idea of generalizing such an approach to an actual unsteady turbulent regime;

– Started to investigate the Hierarchical Model (HiMod) reduction technique to discretize a LES-VMS-SM model with a reduced order model. HiMod reduction is a consolidated technique to model flows exhibiting a dominant flow in the presence of localized transverse dynamics.

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