Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors

This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics. The first part focuses on the steady state of reactors and extends the adjoint sensitivity analysis methods well established for pure neutron transport problems to...

Probabilistic collocation used in a Two-Step approached for efficient uncertainty quantification in computational fluid dynamics

In this paper a Two-Step approach is presented for uncertainty quantification for expensive problems with multiple uncertain parameters. Both steps are performed using the Probabilistic Collocation method. The first step consists of a sensitivity analysis to identify the most important parameters of the problem. The sensitivity derivatives are...

A robust and efficient uncertainty quantification method for coupled fluid-structure interaction problems

A robust and efficient uncertainty quantification method is presented for resolving the effect of uncertainty on the behavior of multi-physics systems. The extrema diminishing method in probability space maintains a bounded error due to the interpolation of deterministic samples at constant phase in a transonic airfoil flutter problem.

Efficient and robust uncertainty quantification for computational fluid dynamics and fluid-structure interaction

Physical uncertainties due to atmospheric variations and production tolerances can nowadays have a larger effect on the accuracy of computational predictions than numerical errors. It is essential to quantify the effect of these uncertainties for reducing design safety factors and robust design optimization. This eventually contributes to the...

A monomial chaos approach for efficient uncertainty quantification on nonlinear problems

A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equations which can be coupled. The proposed monomial...

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

A Monomial Chaos Approach for Efficient Uncertainty Quantification in Computational Fluid Dynamics

A monomial chaos approach is proposed for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can still be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equations which can be coupled. The proposed...

Efficient uncertainty quantification using a two-step approach with chaos collocation

In this paper a Two Step approach with Chaos Collocation for efficient uncertainty quantification in computational fluid-structure interactions is followed. In Step I, a Sensitivity Analysis is used to efficiently narrow the problem down from multiple uncertain parameters to one parameter which has the largest influence on the solution. In Step...

A Monomial Chaos Approach for Efficient Uncertainty Quantification in Computational Fluid Dynamics

A monomial chaos approach is proposed for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can still be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equations which can be coupled. The proposed...

Reliable Computational Predictions by Modeling Uncertainties Using Arbitrary Polynomial Chaos

Inherent physical uncertainties can have a significant influence on computational predictions. It is therefore important to take physical uncertainties into account to obtain more reliable computational predictions. The Galerkin polynomial chaos method is a commonly applied uncertainty quantification method. However, the polynomial chaos...

Reliable Computational Predictions by Modeling Uncertainties Using Arbitrary Polynomial Chaos

Inherent physical uncertainties can have a significant influence on computational predictions. It is therefore important to take physical uncertainties into account to obtain more reliable computational predictions. The Galerkin polynomial chaos method is a commonly applied uncertainty quantification method. However, the polynomial chaos...

Efficient uncertainty quantification using a two-step approach with chaos collocation

In this paper a Two Step approach with Chaos Collocation for efficient uncertainty quantification in computational fluid-structure interactions is followed. In Step I, a Sensitivity Analysis is used to efficiently narrow the problem down from multiple uncertain parameters to one parameter which has the largest influence on the solution. In Step...

A posteriori error analysis for stochastic finite element solutions of fluid flows with parametric uncertainties

Accounting for uncertainty in numerical simulations is a growing concern and a great deal of methods have recently been developed, such as the Polynomial Chaos which basically consists in a spectral approximation of the surface response of the solution by stochastic finite elements. However, criteria for refinement of the spectral space have so...