Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry Original Research Article

The challenges encountered in the development of nodal expansion method (NEM) in cylindrical geometry and the method to circumvent these difficulties are introduced and discussed in this paper. Due to the fact that the azimuthal term contains a factor 1/r2, the traditional transverse integration fails to produce a 1D transverse integrated equation in θ-direction; a simple but effective approach is employed to obtain the θ-directional transverse integration equation. When the traditional polynomials are used to solve the 1D transverse integral equation in r-direction, some additional approximations, which may undermine the precision of the method, are required in the derivation of the moment equations; in order to preserve the accuracy of calculations, the special polynomial approximation is used to solve the 1D transverse integrated equations in r-direction. Moreover, the Row–Column iterative scheme, which is considered to be the more efficient and convenient schemes in cylindrical geometry, is used to solve the partial currents equations. An improved NEM for solving the multidimensional diffusion equation in cylindrical geometry is implemented and tested. And its accuracy and efficiency are demonstrated through several benchmark problems.