Numerical simulations are subject to uncertainties due to the imprecise knowledge of physical properties, model parameters, as well as initial and boundary conditions. The assessment of these uncertainties is required for some applications. In the field of Computational Fluid Dynamics (CFD), the reliable prediction of hydrogen distribution and pressure build-up in nuclear reactor containment after a severe reactor accident is a representative application where the assessment of these uncertainties is of essential importance. The inital and boundary conditions that significantly influence the present buoyancy-driven flow are subject to uncertainties. Therefore, the aim is to investigate the propagation of uncertainties in input parameters to the results variables. As a basis for the examination of a representative reactor test containment, the investigations are initially carried out using the Differentially Heated Cavity (DHC) of aspect ratio 4 with $Ra=2\times {10}^9$ as a test case from the literature. This allows for gradual method development for guidelines to quantify the uncertainty of natural convection flows in large-scale industrial applications. A dual approach is applied, in which Large Eddy Simulation (LES) is used as reference for the Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations. A methodology for the uncertainty quantification in engineering applications with a preceding mesh convergence study and sensitivity analysis is presented. By taking the LES as a reference, the results indicate that URANS is able to predict the underlying mixing process at $Ra=2\times {10}^9$ and the variability of the result variables due to parameter uncertainties.

For the investigation of uncertainties in high dimensional spaces of computationally expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are needed. These methods should provide accurate and efficient High-Dimensional Model Representations of stochastic results using a reasonable number of calculations. Therefore, the PCE–HDMR approach (Polynomial Chaos Expansion–High-Dimensional Model Representation) is utilized to qualify appropriate UQ methods for large-scale computations in the field of Computational Fluid Dynamics. This technique is a combination of Cut-HDMR, a hierarchical decomposition modeling approach, with PCE. To demonstrate its effectiveness, the PCE–HDMR methodology in conjunction with complementary modeling techniques is applied for the UQ analysis of a buoyancy-driven mixing process between two miscible fluids within the Differentially Heated Cavity of aspect ratio 4. The results include a thorough probabilistic representation of time-dependent response quantities that comprehensively describe the mixing process. The stochastic models are derived from Large Eddy Simulations using PCE–HDMR and the Sparse Grid Method, which serves as a reference for the results from PCE–HDMR. The results show that PCE–HDMR provides accurate statistics of the modeled time-dependent stochastic processes and shows good agreement with the reference results. Thus, PCE–HDMR indicates great potential for UQ of technical-scale computations due to its efficiency and flexibility in the construction of stochastic models.

For the investigation of uncertainties in high dimensional spaces of computationally expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are needed. These methods should provide accurate and efficient High-Dimensional Model Representations (HDMR) of stochastic results using a reasonable number of calculations. Therefore, the PCE-HDMR approach is utilized to qualify appropriate UQ methods for large-scale computations in the field of Computational Fluid Dynamics (CFD). This technique is a combination of Cut-HDMR, a hierarchical decomposition modeling approach, with Polynomial Chaos Expansion (PCE). To demonstrate its effectiveness, the PCE-HDMR methodology in conjunction with complementary modeling techniques is applied for the UQ analysis of a buoyancy-driven mixing process between two miscible fluids within the Differentially Heated Cavity (DHC) of aspect ratio 4. The results include a thorough probabilistic representation of time-dependent response quantities that comprehensively describe the mixing process. The stochastic models are derived from Large Eddy Simulations (LES) using PCE HDMR and the Sparse Grid Method (SGM), which serves as a reference for the results from PCE-HDMR. The results show that PCE-HDMR provides accurate statistics of the modeled time-dependent stochastic processes and shows good agreement with the SGM reference. Thus, PCE-HDMR indicates great potential for UQ of technical-scale computations due to its efficiency and flexibility in the construction of stochastic models.