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This study is part of a national (ANR) research program entitled QUTE-HPC (QUantum Turbulence Exploration by High-Performance Computing). The project gathers 10 researchers from physics and mathematics and is aimed at providing a new state-of-the-art for the mathematical-physical modelling and High Performance Computing (HPC) of Quantum Turbulence (QT) in superfluid quantum fluids, such as superfluid Helium (He) and atomic Bose-Einstein condensates (BEC). The primary focus of the project is the study of QT in liquid Helium. More information on the project can be find at http://qute-hpc.math.cnrs.fr/