Comparison of polynomial chaos expansion methods for uncertainty quantification in computational fluid dynamics simulations

Abstract

Computational Fluid Dynamics (CFD) computer codes have proven to be a powerful tool in the analysis of all kinds of fluid systems. However, there is still a lack of practical methods for determining the uncertainty of their results, as most current techniques require performing too many simulations to be affordable in industrial-scale situations. One of the most promising methods for uncertainty quantification in computational fluid dynamics is Polynomial Chaos Expansion, a name that includes a variety of techniques, all based on the same mathematical background: projecting the system’s response into a basis of orthogonal polynomials. This paper discusses the main advantages and drawbacks of three of these techniques, namely random sampling, Gaussian quadrature and linear regression, in terms of reliability, ease of use and computational costs. All three techniques were applied to simulations of the turbulent mixing of two streams of water inside a Y-shaped channel, and the results compared with experimental data. Results show that, in this test case, quadrature method provides more reliable results than the other two techniques, with a lower computational cost. Due to its robustness and low number of simulations required, Polynomial Chaos Expansion via quadrature methods might be suitable for most industrial CFD simulations.