A one-dimensional polynomial chaos method in CFD–Based uncertainty quanti-fication for ship hydrodynamic performance

A one-dimensional non-intrusive Polynomial Chaos (PC) method is applied in Uncertainty Quantification (UQ) studies for CFD–based ship performances simulations. The uncertainty properties of Expected Value (EV) and Standard Deviation (SD) are evaluated by solving the PC coefficients from a linear system of algebraic equations. The one-dimensional PC with the Legendre polynomials is applied to: (1) stochastic input domain and (2) Cumulative Distribution Function (CDF) image domain, allowing for more flexibility. The PC method is validated with the Monte-Carlo benchmark results in several high-fidelity, CFD-based, ship UQ problems, evaluating the geometrical, operational and environmental uncertainties for the Delft Catamaran 372. Convergence is studied versus PC order P for both EV and SD, showing that high order PC is not necessary for present applications. Comparison is carried out for PC with/without the least square minimization when solving the PC coefficients. The least square minimization, using larger number of CFD samples, is recommended for current test cases. The study shows the potentials of PC method in Robust Design Optimization (RDO) and Reliability-Based Design Optimization (RBDO) of ship hydrodynamic performances.