Second order perturbation theory for nonlinear time-dependent problems: Application to a simplified coupled transient

In this paper a second-order perturbation technique for nonlinear time-dependent problems is presented and applied to a simplified multi-physics model. This method is developed by using the properties of the adjoint problem which allows calculating the set of first and second order coefficients by solving a number of linear systems. As an illustrative example the adjoint procedure is applied to a reference transient problem, represented by a coupled point-kinetic/lumped-parameters model, and used to calculate the sensitivity coefficients of a safety related response with respect to a set of input parameters. The results obtained are compared with the values given by a direct sampling of the forward nonlinear problem. A way to reduce the number of calculations required for the application of second order adjoint techniques is also discussed. Our first results show that the procedure provides good estimations in presence of higher order perturbation components, being able to reconstruct the responses of interest even in presence of non-Gaussian probability density functions. Furthermore, the use of reduced second order information decreases the computational requirements of the method, making it appealing for possible large scale applications. (authors)