Scilab for uncertainty in simulations: some numerical applications of the Polynomial Chaos Expansion method

Gregorio Pellegrini

University of Verona


In many real world applications a certain lack of knowledge could characterize the model of a given process through uncertainties of the parameters involved. Hence a single deterministic numerical simulation may not be enough to describe a certain physical phenomenon. Thus we move toward Uncertainty Quantification (UQ) methods, in particular analyzing the so-called Polynomial Chaos Expansion (PCE) technique which provides an enhanced approach, with respect to standard Monte-Carlo methods, to deal with uncertainties in simulations.

We present such technique by means of non-trivial numerical applications, exploiting the Non-Intrusive Spectral Projection (NISP) toolbox for Scilab, which implements the PCE in such environment.

In particular, we focus our attentions on solving a 2-dimensional Computational Fluid Dynamics problem as well as a couple of 2-dimensional advections problems in presence of uncertain parameters, highlighting both the flexibility of NISP toolbox, which interacts with several data sources, and its efficiency in detecting the required solution.