Multi-fidelity modelling for flow over a cylinder

We tackle the classical problem of predicting the relation between C$_{\mathrm{L}}$, C$_{\mathrm{D}}$ and C$_{\mathrm{P}}$ vs Reynolds number for flow over cylinder using the multi-fidelity framework. The stochastic response surface is obtained by implementing the auto-regressive stochastic modelling (Kennedy and O'Hagan, 2000) and Gaussian process regression to combine data from variable levels of fidelity. In particular, we predict the lift, drag and pressure coefficients where codes with multiple levels of fidelity are available. We correlate data at each of these levels and build the surrogate model using multi-level recursive co-kriging. The deficient physics of the low-fidelity model is explored by examining the cross-correlation between the low-fidelity and high-fidelity models. The proposed framework ultimately intends to meld computational accuracy of the expensive high fidelity with the computational cost of the inexpensive low-fidelity.