The numerical solution of space-dependent neutron kinetics equations in hexagonal-z geometry using Diagonally Implicit Runge Kutta method

The numerical solution of the space-dependent neutron kinetics equations in hexagonal-z geometry is studied in this paper. The equations are discretized by Diagonally Implicit Runge-Kutta (DIRK) method in the temporal direction. The semi-discretized equations are in the form of the fixed source problems, which can be solved by the function expansion nodal method in the hexagonal-z geometry. The intranodal fluxes in each group are expanded by exponential functions and orthogonal polynomials up to the second order. The two-and three-dimensional benchmark problems are used to verify this method. Compared with the backward Euler method, the numerical results show that the current method is more accurate.