Turbulent flows are a classical example of multi-scale complex physical systems. Due to the expensive cost of high-fidelity simulations to resolve all scales, Reynolds-Averaged Navier-Stokes (RANS) simulations are still widely used in engineering applications. However, it is well known that RANS models have large model-form uncertainties, which diminish their predictive capabilities. In this talk, I will introduce two data-driven frameworks to improve RANS models. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high-fidelity simulation databases. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled.
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