Application of a Mesh Free Method Based on the Wendland Radial Basis Functions to Solve the Neutron Diffusion Equation in Two-Dimensional Geometry

These days, application of mesh free methods in the areas of numerical analysis and computational sciences has been the subject of many researches. In this paper, the mesh free method based on the point interpolation scheme is used to solve the one-group neutron diffusion equation in a two- dimensional Cartesian coordinate system. The Wendland type radial basis functions were applied to perform the interpolations. The Galerkin method was employed to discretise the weak form of the neutron diffusion equation. In order to calculate the integrations of the weak form of the equations, Gauss-Legendre scheme was applied. The efficiency and accuracy of the method was evaluated through a number of case studies. The results were compared with the analytical solutions. For the cases where the numerical solutions did not exist, the problem was simulated through the Citation code and the results were compared, accordingly. The Reed test problem was solved to show the performance of the developed code. A PWR reactor core was also simulated through the introduced method. The effect of combination of different Wendland functions with polynomial functions on the accuracy of the results was also assessed. There is a good agreement between the numerical and the analytical solutions, and also the result from the Citation code revealed the accuracy of the method, and the good performance of the applied method was also confirmed in this study. At last, the developed method introduced in this work was found to be applicable to implement the desired nuclear computational codes.