A three-dimensional nodal neutron kinetics code with a higher-accuracy algorithm for reactor core in hexagonal-z geometry

A nodal neutron kinetics model with a higher-accuracy algorithm for three-dimensional multi-group neutron diffusion calculation is developed for transient analysis of reactor core in hexagonal-z geometry. The spatial discretization technique is based on a high order nodal expansion method for hexagonal-z geometry. In this method, one dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four order polynomial expansion respectively. The partially-integrated radial and axial leakages are both approximated by the quadratic polynomial. The time discretization technique is based on a fully implicit scheme combined with a Runge-Kutta method for solving the neutron flux and delayed neutron precursor equations. A flux weighting method is adopted to calculate homogenized multi-group cross sections for transient analysis of control rod ejection accident. The described numerical methods are implemented into the computer code HNHEXK. This code is tested with one static benchmark problem and several kinetic benchmark problems. The numerical results show that the current method has a good agreement with the reference.