  This paper presents a comparison of two multi-fidelity methods for the
forward uncertainty quantification of a naval engineering problem.
Specifically, we consider the problem of quantifying the uncertainty of the
hydrodynamic resistance of a roll-on/roll-off passengers ferry advancing in
calm water and subject to two operational uncertainties (ship speed and
payload). The first four statistical moments (mean, variance, skewness,
kurtosis), and the probability density function for such quantity of interest
(QoI) are computed with two multi-fidelity methods, i.e., the Multi-Index
Stochastic Collocation (MISC) method and an adaptive multi-fidelity Stochastic
Radial Basis Functions (SRBF) algorithm. The QoI is evaluated via computational
fluid dynamics simulations, which are performed with the in-house unsteady
Reynolds-Averaged Navier-Stokes (RANS) multi-grid solver $\chi$navis. The
different fidelities employed by both methods are obtained by stopping the RANS
solver at different grid levels of the multi-grid cycle. The performance of
both methods are presented and discussed: in a nutshell, the findings suggest
that, at least for the current implementations of both algorithms, MISC could
be preferred whenever a limited computational budget is available, whereas for
a larger computational budget SRBFs seem to be preferable, thanks to its
robustness to the numerical noise in the evaluations of the QoI.
