Development of a neutron diffusion solver using the finite volume method

In this thesis, a Python 3.9.4-based, modular, and open-source computational tool was developed to solve two group neutron diffusion equations for three-dimensional reactor geometries using the finite volume method (FVM). The original contribution of this work lies in providing an integrated workflow capable of automatically generating group cross sections with the Serpent code even for complex geometries, reading these cross sections, constructing the FVM coefficient matrix, and solving the eigenvalue-eigenvector problem in a memory efficient manner. At the input stage, the user loads a mesh file in .vtk format into the program, generated by SALOME or OpenFOAM/snappyHexMesh. The software defines cubic boundary surfaces for each cell and automatically produces Serpent surf, cell, and gcu cards, thereby modeling each cell as a separate "void universe" and obtaining localized group cross sections. The group cross-section .m outputs generated by Serpent are converted into JSON format containing only the required variables, minimizing memory usage. Using the JSON data and mesh geometry, diffusion, absorption, scattering, and fission coefficients are calculated and combined with directional neighbor information to construct a sparse block matrix structure. The resulting generalized eigenvalue problem is solved using SciPy's LU decomposition and Arnoldi-based eigs solver, yielding the system's effective multiplication factor (keff) and group-wise neutron flux distributions. Solution vectors are rewritten into .vtk files via PyVista, enabling direct inspection in visualization environments such as ParaView. Compared to equivalent Monte Carlo analyses, the developed method produces results in several orders of magnitude faster, and the obtained cell-wise power distributions can be coupled with thermal hydraulic codes, paving the way for multi-physics studies. Thus, a fast, flexible, and extensible computational infrastructure has been established for reactor core design and analysis processes. For validation, several simple geometries were first tested, followed by comparison with an High Temperature Test Reactor (HTTR) reactor analysis. The results showed that the developed computational tool provides acceptable results.