Hybrid finite-element-based numerical solution of the multi-group SP3 equations and its application on hexagonal reactor problems

•A hybrid finite element nodal solution of the SP3 equations was developed.•Discontinuity factors and parallelization are easily applicable in the algorithm.•The developed algorithm was verified on the Hébert academic benchmark problem.•Diffusion and SP3 solutions were compared on a VVER-440 benchmark problem.•The effect of considering higher-order anisotropic scattering was analyzed. The C-PORCA reactor physics code of the Paks Nuclear Power Plant performs three-dimensional, two-group diffusion calculations applying parametrized group constants generated by the HELIOS code. To improve the accuracy of the calculations, the C-PORCA code was extended with a simplified spherical harmonics module. This paper presents the applied finite-element-based solution algorithm of the SP3 equations in response matrix formalism. Radially primal mixed-hybrid finite element method is used for response matrix calculation with the inclusion of Lagrange multipliers to enforce nodal balance on each element. The axial solution is analytically performed connecting the axial and radial directions through radial leakage with transverse integration. Coupling between the adjacent volumetric elements is performed with node-to-node axial and radial partial current-like moment iterations, that enables the application of SP3 discontinuity factors and the parallelization of the calculation process. The accuracy of the SP3 solution algorithm is demonstrated on academic benchmark and VVER-440 core calculations.