Stochastic Data-Driven POD-Based Modeling for High-Fidelity Coarsening of Two-Dimensional Rayleigh-Bénard Turbulence

A stochastic data-driven based model is proposed to augment coarse-grid numerical simulations of two-dimensional Rayleigh-Bénard convection. Proper orthogonal decomposition (POD) is used to decompose fine-grid reference data into spatial fields and temporal coefficients. The latter are modeled as stochastic processes, yielding a model with few tunable parameters. A relatively small number of POD modes is found to be sufficient to obtain accurate Nusselt number estimates at Rayleigh number \(10^{10}\) .