Data-driven spectral turbulence modelling for Rayleigh-Benard convection

A data-driven turbulence model for coarse-grained numerical simulations of two-dimensional Rayleigh-Benard convection is proposed. The model starts from high-fidelity data and is based on adjusting the Fourier coefficients of the numerical solution, with the aim of accurately reproducing the kinetic energy spectra as seen in the high-fidelity reference findings. No assumptions about the underlying partial differential equation or numerical discretization are used in the formulation of the model. We also develop a constraint on the heat flux to guarantee accurate Nusselt number estimates on coarse computational grids and high Rayleigh numbers. Model performance is assessed in coarse numerical simulations at Ra = 10(10). We focus on key features including kinetic energy spectra, wall-normal flow statistics and global flow statistics. The method of data-driven modelling of flow dynamics is found to reproduce the reference kinetic energy spectra well across all scales and yields good results for flow statistics and average heat transfer, leading to computationally cheap surrogate models. Large-scale forcing extracted from the high-fidelity simulation leads to accurate Nusselt number predictions across two decades of Rayleigh numbers, centred around the targeted reference at Ra = 10(10).

Automated summary

This study proposes a data-driven turbulence model for coarse-grained numerical simulations of two-dimensional Rayleigh-Benard convection. The model is based on high-fidelity data and adjusts the Fourier coefficients of the numerical solution to accurately reproduce the kinetic energy spectra observed in the reference findings. The model does not rely on assumptions about the partial differential equation or numerical discretization. A constraint on the heat flux is also introduced to ensure accurate Nusselt number estimates at coarse computational grids and high Rayleigh numbers. The performance of the model is assessed in coarse numerical simulations at Ra = 10(10), and it is found to accurately reproduce the reference kinetic energy spectra and yield good results for flow statistics and average heat transfer. The large-scale forcing extracted from the high-fidelity simulation leads to accurate predictions of Nusselt numbers across a wide range of Rayleigh numbers centered around Ra = 10(10).