THE EVEN-PARITY AND SIMPLIFIED EVEN-PARITY TRANSPORT-EQUATIONS IN 2-DIMENSIONAL X-Y GEOMETRY

The finite element and lumped finite element methods for the spatial d ifferencing of the even-parity discrete ordinates neutron transport eq uations (EPS(N)) in two-dimensional x-y geometry are applied. In addit ion, the simplified even-parity discrete ordinates equations (SEPS(N)) as an approximation to the EPS(N) transport equations are developed. The SEPS(N) equations are more efficient to solve than the EPS(N) equa tions due to a reduction in angular domain of one-half, the applicabil ity of a simple five-point diffusion operator, and directionally uncou pled reflective boundary conditions. Furthermore, the SEPS(N) equation s satisfy the same diffusion limits as EPS(N) in an optically thick re gime, appear to have no ray effect, and converge faster than EPS(N) wh en using a diffusion synthetic acceleration (DSA). Also, unlike the ca se of EPS(N), the SEPS(N) solutions are strictly positive, thus requir ing no negative flux fixups. It is also demonstrated that SEPS(N) is a generalization of the simplified P-N method. Most importantly, in the se second-order approaches, an unconditionally effective DSA scheme ca n be achieved by simply integrating the differenced EPS(N) and SEPS(N) equations over the angles. It is difficult to obtain a consistent DSA scheme with the first-order S-N equations. This is because a second-o rder DSA equation must generally be derived directly from the differen ced first-order S-N equations.