A Hybrid Nodal Diffusion/SP₃ Method Using One-Node Coarse-Mesh Finite Difference Formulation

Abstract

A hybrid nodal diffusion/simplified P₃ (SP₃) method was implemented within the framework of a one-node coarse-mesh finite difference formulation. The one-node formulation enables the use of various combinations of space, energy, and angular approximations within the framework of the one-node global/local solution approach. Spatial approximations include advanced nodal methods and fine-mesh finite difference methods. Energy approximations involve conventional two-group and multiple energy groups. Angular approximations contain both the diffusion and SP₃ methods. Partial-moment boundary conditions are used to solve the one-node problems since they simplify the formulation of consistent interface conditions for the various methods. All directional moments are determined simultaneously to stabilize convergence of the one-node global/local solution approach. Results for a light water reactor mixed-oxide benchmark problem indicate that the hybrid application of the one-node-based nodal SP₃ method developed here can provide substantial reductions in the computational time without compromising the accuracy of the solution.