• polynomial chaos expansion
• roughness
• turbulence

In the present thesis a stochastic methodology is proposed to estimate aerodynamic quantities characterizing the flow over a rough surface.
An irregular rough surface is considered, whose geometrical parameters are characterized through a given Probability Density Function (PDF). The parameter space is sampled through the Latin Hypercube Sampling (LHS) method and a stochastic surrogate model is used to calculate the response function at each sample point, thus avoiding the need of carrying out computationally expensive wall resolved numerical simulations. The response surrogate model in the parameter space of the quantities of interest is built by using the Polynomial Chaos Expansion (PCE) starting from a few Direct Numerical Simulations (DNS) of sinusoidal rough wall geometries. Collecting the responses of all the samples with a statistical approach, the PDF of the quantities of interest, as well as their mean value and standard deviation, are reconstructed for the given irregular roughness. In the present study, only the variability of the streamwise wavelength has been taken into account to validate the procedure.
To assess the validity of the method, the drag coefficient, roughness function and turbulence intensities obtained with the stochastic approach are compared with those obtained in corresponding wall resolved DNS and a good agreement is obtained.
The computationally efficient and inexpensive prediction model is then thought to provide the quantities of quantities that characterize the flow to larger scale models
where the topography of the surfaces cannot be simulated due the grid resolution.