Consistent $\mathrm{P_1}$ Synthetic Acceleration of Inner Transport Iterations in $\mathrm{3D}$ Geometry

For the $\mathrm{KP_1}$ iterative transport method the production procedure of its “$\mathrm{P_1}$” step consistent with an arbitrary spatial approximation of the $\mathrm{S_N}$ transport equation in $\mathrm{3D}$ Cartesian geometry is presented. The procedure is applied to the nodal schemes approximating the within-group $\mathrm{S_N}$ transport equation on the unstructured tetrahedral mesh. Produced $\mathrm{P_1}$ synthetic accelerations are experimentally shown to be numerically effective on several model problems.