Improved approximations applied to the S(sub N) even-parity equation

摘要

We have developed various finite element differencing schemes by applying lumping techniques in neutron streaming and removal terms of the S(sub N) even-parity transport equation in two-dimensional x-y geometry. We have derived an analytical form of the even-parity reflective boundary condition, which along with the vacuum boundary condition can be applied directly to solve second-order even-parity boundary value problems. We have also developed a new simplified even-parity equation that is much more computationally efficient than the even-parity equation. The developed schemes are numerically compared with the conventional first-order diamond-differencing (DD) scheme.