An improved Random Fourier Method with physics informed learning for turbulence generation
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The generation of synthetic turbulence as initial or boundary conditions is a key ingredient to capture the dynamics of turbulent flows in large eddy simulation. Among existing approaches, the superposition of random Fourier modes known as RFM method originally proposed by Kraichnan [1] for homogeneous and isotropic turbulence provides a rather simple way to obtain a divergence-free velocity field with a prescribed kinetic energy spectrum. Various extensions have been proposed to deal with anisotropy [2] and unsteadiness [3]. However, the standard RFM formulation is known to reproduce mainly low order statistics, while higher order features such as intermittency remain poorly captured or absent [4]. It is expected that these discrepancies have a major impact on the adjustment periods and establishment lengths observed in the simulations. This contribution explores physics informed optimization strategies aimed at improving the statistical representativeness of RFM. The proposed approach relies on the parametric adjustment of selected Fourier mode characteristics, guided by loss functions solely derived from turbulence properties such as spectral constraints and higher order velocity increment statistics. The methodology is investigated within the frame of homogeneous isotropic turbulence. In addition to analyzing statistical consistency at the field generation level, the impact of the resulting increment probability density functions is assessed in simulations of decaying isotropic turbulence, in comparison with standard RFM relying on Gaussian higher order moments.
