Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere

Sagy Ephrati; Paolo Cifani; Milo Viviani; Bernard Geurts

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arXiv · 2304.12007

Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere

Sagy Ephrati·Paolo Cifani·Milo Viviani·Bernard Geurts

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Abstract

A resolution-independent data-driven stochastic parametrization method for subgrid-scale processes in coarsened fluid descriptions is proposed. The method enables the inclusion of high-fidelity data into the coarsened flow model, thereby enabling accurate simulations also with the coarser representation. The small-scale parametrization is introduced at the level of the Fourier coefficients of the coarsened numerical solution. It is designed to reproduce the kinetic energy spectra observed in high-fidelity data of the same system. The approach is based on a control feedback term reminiscent of continuous data assimilation. The method relies solely on the availability of high-fidelity data from a statistically steady state. No assumptions are made regarding the adopted discretization method or the selected coarser resolution. The performance of the method is assessed for the two-dimensional Euler equations on the sphere. Applying the method at two significantly coarser resolutions yields good results for the mean and variance of the Fourier coefficients. Stable and accurate large-scale dynamics can be simulated over long integration times.

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Sagy Ephrati, Paolo Cifani, Milo Viviani, Bernard Geurts. 2023-04-24. Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere. https://arxiv.org/abs/2304.12007

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