A quasi-static approach for the solution of steady-state linear transport problems

This work was originally motivated by a research challenge formulated by prof. Ravetto more than a decade ago, on whether it is possible to adapt the quasi-static (QS) method for the solution of steady-state linear transport equation. As explained in this paper, several non-trivial technicalities arise when trying to apply projection techniques in a QS fashion to time-independent problems. After outlining how the shape/amplitude factorization can be extended to steady-state problems based on heuristic observations, we derive a hybrid method combining classical transport techniques with the QS approach. This methodology is tested in several one-dimensional test cases, to investigate the numerical performance of this novel approach and its convergence properties against a classical solution technique (i.e. discrete ordinates, using diamond difference and finite volumes).