Simplified P ₃ neutron transport calculation based on Smoothed particle hydrodynamics with second-order accuracy for second derivatives

In order to facilitate the treatment of deformed geometries for the multiphysics simulation in reactor physics, the Smoothed Particle Hydrodynamics (SPH) method is applied to the Simplified P3 (SP3) neutron transport calculation. To accurately perform the SP3 neutron transport calculation, the SPH method with second-order accuracy for second derivatives, denoted as SPH(2), is utilized to reduce discretization errors, especially those arising from irregular particle arrangements. Furthermore, the space-dependent kinetics calculation is implemented using Proper Orthogonal Decomposition (POD) with an on-the-fly procedure. The developed code was verified in a two-dimensional xy geometry through the ramp transient case of the TWIGL benchmark problem, by comparing the numerical results with reference values obtained by MOC with the Multigrid Amplitude Function (MAF) method. Consequently, this study demonstrated that the numerical results of keff using SP3-SPH(2) agreed well with the reference MOC calculation, even for irregular particle arrangements. Thanks to the application of SPH(2), average biases and standard deviations in the numerical results of both criticality and kinetics calculations were successfully reduced as the particle size decreased, which could not be achieved using the conventional SPH method.