
A Hierarchical Model (HiMod) reduction for the simulation of turbulent flows in solar panels
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Hierarchical Model (HiMod) reduction is a methodology to simulate phenomena with a dominant directionality, encountered in real scenarios such as hemodynamics, acoustic wave propagation, industrial circuit or pipeline optimization. Despite the presence of a main direction, these problems remain inherently three-dimensional, leading to computationally anaffordable simulations. HiMod exploits the separation of variables principle to discretize the dynamics aligned with the mainstream through an IsoGeometric Analysis, while employing a modal expansion to solve the transverse dynamics. This strategy simplifies a full-order (3D or 2D) problem into a system of coupled 1D equations [1], significantly reducing computational cost while preserving accuracy, as demonstrated across different application fields [2, 3]. The efficiency of HiMod reduction is particularly enhanced by the use of a customized modal basis whose functions are the solution to a carefully chosen Sturm-Liouville eigenvalue problem, directly related to the specific model being reduced [4]. In this work, we apply HiMod discretization to solve turbulent flows in solar panel pipelines, using a newly developed set of modal basis functions specifically designed for this context. REFERENCES [1] S. Perotto, A. Ern, and A. Veneziani, Hierarchical local model reduction for elliptic problems: a domain decomposition approach, Multiscale Model. Simul., 8.4, 1102–1127, (2010). [2] Y. A. Brandes Costa Barbosa and S. Perotto, Hierarchically reduced models for the Stokes problem in patient-specific artery segments, Int. J. Comput. Fluid Dyn., 34.2, 160–171, (2020). [3] G. G. Gentili, M. Khosronejad, G. Bernasconi, S. Perotto, S. Micheletti, Efficient modeling of multimode guided acoustic wave propagation in deformed pipelines by hierarchical model reduction, Appl. Numer. Math., 173, 329–344, (2022). [4] M. C. Aletti, S. Perotto, and A. Veneziani, HiMod reduction of advection- diffusion reaction problems with general boundary conditions, J. Sci. Comput., 76.1, 89–119, (2018).