A more efficient implementation of the discrete-ordinates method for an approximate model of particle transport in a duct

•Method of doubling solution for the pipe problem.•Uses convergence acceleration.•Fully discretized solution.•Improvement over ADO.

We consider transport of light, neutrons, or any uncharged particles in a straight duct of circular cross section. This problem first came to fashion some 30 years ago when Pomraning and Prinja formulated their so called “pipe problem”. In the years to follow, investigators applied essentially every known method of numerical solution, including MMRW’s Wiener–Hopf – except possibly one. This presentation concerns that particular numerical solution, which arguably seems to be the most efficient of all.