A nodal P₁ two-step method for PWR-core neutronics calculation

To address the challenges of anisotropic scattering in Pressurized Water Reactor (PWR) core neutronics calculations, a two-step nodal method based on the P₁ theory, named the nodal P₁ two-step method, is proposed. A rigorous derivation of the second-order steady-state P₁ equation is presented, which incorporates an additional first-order source term to account for the coupling of leakage fluxes between energy groups. A P₁ variational nodal method is established to solve this equation. Furthermore, a homogenization theory is established, utilizing angle-dependent diffusion coefficient matrices and Discontinuity Factors to guarantee the conservation of reaction rates and net surface currents. The proposed method is implemented in the PWR-core reactor physics analysis code NECP-Bamboo. Verifications against diffusion benchmarks, 2 × 2 assembly, 2D mini-core problems and 3D MTR problem demonstrate that the nodal P₁ two-step method significantly outperforms the conventional diffusion method. While improvements in effective multiplication factor were from 2 to 934 pcm, the method substantially enhanced fission rate distribution accuracy in regions with strong anisotropic scattering, reducing maximum deviations at fuel-reflector interfaces from 2.26% to 1.12%. Crucially, these gains are achieved with a computational overhead of increasing approximately 6.8%, demonstrating that the nodal P₁ two-step method offers a viable alternative for routine engineering applications.