Projection-based second order perturbation theory

Highlights: ► A new approach to calculate second order variations using variational theory is presented. ► The approach employs only first order variations in tandem with matrix decomposition methods. ► Regularization of second order derivatives is employed to minimize effect of numerical errors. ► Representative numerical experiments are given. -- Abstract: Reactor analysis represents a typical example of a complex engineering system that is described by multi-scale and multi-physics nonlinear models with many input parameters and output responses. Obtaining reference solutions to these models is computationally expensive which renders impractical their repeated executions for engineering-oriented studies such as design optimization, uncertainty quantification, and safety analysis. To overcome this challenge, sensitivity analysis based on first-order perturbation theory has been widely used in the reactor analysis community to estimate changes in responses of interest due to input parameter variations. Although perturbation theory has been rigorously developed over the past four decades in order to extend its applicability to estimate higher order variations, engineering applications have primarily focused on first-order perturbation theory only. This is because the computational overhead of higher order perturbation theory are often overwhelming and do not justify the development effort required for their implementation. This manuscript further develops a recently introduced higher order approach to estimate second order variations. The objective is to demonstrate that first-order perturbation theory can be employed in practical engineering calculations to estimate higher order variations. The applicability of the introduced approach is analyzed with TSUNAMI-2D for typical lattice physics calculations.