Nodal transport methods are proposed for solving the simplified even-parity neutron transport (SEP) equation. These new methods are attributed to the success of existing nodal diffusion methods such as the Polynomial Expansion Nodal and the Analytic Function Expansion Nodal Methods, which are known to be very effective for solving the neutron diffusion equation. Numerical results show that the simplified even-parity transport equation is a valid approximation to the transport equation and that the two nodal methods developed in this study also work for the SEP transport equation, without conflict. Since accuracy of methods is easily increased by adding node unknowns, the proposed methods will be effective for coarse mesh calculation and this will also lead to computation efficiency.

To correctly predict the neutron behavior based on diffusion calculations, it is necessary to adopt well-specified boundary conditions using suitable diffusion approximations to transport boundary conditions. Boundary conditions such as the zero net-current, the Marshak, the Mark, the zero scalar flux, and the Albedo condition have been used extensively in diffusion theory to approximate the reflective and vacuum conditions in transport theory. In this paper, we derive and analyze these conditions to prove their mathematical validity and to understand their physical implications, as well as their relationships with one another. To show the validity of these diffusion boundary conditions, we solve a sample problem. The results show that solutions of the diffusion equation with these well-formulated boundary conditions are very close to the solution of the transport equation with transport boundary conditions.