Adjoint-Based Sensitivity for Radiation Transport Using an Eddington Tensor Formulation

Adjoint methods can provide a first-order approximation of the response a physical system experiences due to a perturbation in the system’s parameters. However, when applying the method to time dependent transport, memory costs can quickly become a concern, and a fully angular dependent flux must be stored at each timestep. In this thesis, a lower-order Variable Eddington Tensor formulation of the transport equation is considered to remove the angular dependence of the stored solution and reduce memory costs. Indeed, given the Eddington tensor, the Eddington tensor approach yields the same flux solution as the full transport solution. In the case of perturbations, one may make some simplifying assumption regarding the Eddington tensor: for instance, keep it unperturbed or assuming a functional variation of the Eddington tensor over the input parameter space. An unperturbed Eddington assumption may introduce error in the sensitivity calculation. A simple linear interpolation scheme for the Eddington over the uncertain parameter range is devised for use in certain scenarios, at the cost of requiring a few additional angular solves to parameterize the Eddington tensor. An alternate formulation using an Eddington tensor derived from the adjoint transport is also presented. Comparison of the derived Eddington methods and transport methods is done using simple slab geometry test cases