With the development of nuclear-thermal coupling technology, it is essential to consider the strong coupling effects between multiple physics fields and achieve high precision and large-scale parallel computing. Simultaneous solutions to the conservation equations of multiple physics fields need to be pursued, providing a unified approach to modeling, discretization, and iterative computation processes.

This study aims to achieve discrete and iterative solutions for multigroup neutron diffusion equations and neutron transport equations, considering the strong coupling between neutronics and thermal-hydraulics.

Firstly, based on the open-source computational fluid dynamics (CFD) platform OpenFOAM, the finite volume method (FVM) was employed to discretize the control equations for neutron diffusion and neutron transport using the Gauss theorem. Then, the discrete ordinates method was applied to the discretization of the neutron transport equation for spatial angular discretization, and FVM was used to discretize both neutron diffusion and neutron transport equations spatial variables whilst the multigroup method was employed for discretizing energy variables, and implicit Euler method was utilized for discretizing time variables. Finally, neutron diffusion was verified using three benchmark cases, i.e., two-dimensional International Atomic Energy Agency (IAEA), three-dimensional IAEA, and three-dimensional LMW, to validate the effectiveness of the developed program, and neutron transport was verified using various benchmark cases including IAEA, TAKEDA, and C5G7.

The verification results for the two-dimensional IAEA benchmark show excellent agreement, with a maximum error of 1.1% in normalized power. The three-dimensional IAEA benchmark results align closely with reference values, showing a maximum error of 3.4%. For the three-dimensional LMW benchmark, the total power at 20 s is slightly underestimated, with a maximum error below 2%. The IAEA criticality benchmark results show region-averaged flux and effective multiplication factor deviations of 6.9% and 22×10^-?, respectively. The TAKEDA benchmark confirms the program's accuracy in three-dimensional problems, with effective multiplication factor, neutron flux, and control rod worth matching reference values. The C5G7 benchmark validates the FVM-based transport algorithm's strong geometric adaptability and ability to solve both uniform and non-uniform neutron physics problems accurately.

FVM-based neutron diffusion and transport algorithms developed in this study lay the foundation for the future simultaneous solution of conservation equations for physical and thermal multi-physics fields under a unified programming framework. The integrated verification of neutron diffusion and transport programs underscores the reliability and flexibility of the FVM in accurately solving complex neutron transport and diffusion scenarios, providing a pathway for enhancing precision and computational efficiency in nuclear engineering simulations under a unified programming framework.