Synthesis of Three-Dimensional Transport Problems Using Two-Dimensional Trial Functions

Two schemes are proposed in which solutions to the three-dimensional transport equation can be synthesized from two-dimensional transport solutions. Derivations are presented which employ a weighted residual technique applied to the second order (even parity in the direction vector Ω) form of the transport equation. Numerical testing indicates that for problems in which transport effects are restricted to the trial function planes, where synthesis axis leakage can be described by diffusion theory, the transport synthesis schemes perform very well.