Adjoint Sensitivity Analysis of a 1D Stationary Neutronics–Thermal Hydraulics–Coupled Molten Salt Reactor Model

In sensitivity analysis, adjoint methods are the most efficient for complex systems with many input parameters and few output responses, such as reactor physics problems. In this context, this work presents an adjoint sensitivity analysis method for a one-dimensional model of a stationary neutronics–thermal hydraulics–coupled molten salt reactor (MSR), using the Lagrangian formalism most commonly used in the field of optimization. Focusing on the specific case of a response function dependent only on the effective multiplication factor k_eff (such as the reactivity), the model is implemented numerically in Python. The results are discussed using molten salt fast reactor data. The adjoint problem is solved through a partitioned scheme. In particular, the singular adjoint neutronics problem is solved using eigenvalue shifting. Various adjoint sensitivities are evaluated and are found to agree with reference finite differences calculations, showing the potential of adjoint methods for the multiphysics of MSRs. As calculating partial derivatives is complex and error prone, automatic differentiation should be considered in future work.