An optimized sweeping solution method for the three-dimensional Sn equations of neutron transport on hexahedral meshes

•An optimized sorting algorithm is proposed to remove deadlock without searching for global dependent cycles.•The effective face method is applied in the spatial discretization to deal with the integrals on the non-planar cell faces.•The convergence of the splitting iterative algorithm is proved rigorously.•The new method is verified to be conducive to the convergence of the iteration by numerical experiments.•Numerical results show the effectiveness and high efficiency of the new algorithm on general hexahedral meshes.