Numerical methods in the KIKO3d three-dimensional reactor dynamics code

This paper reviews the numerical methods applied in the KIKO3D threedimensional reactor dynamics code. First we consider some simple solution methods for the static neutronic diffusion equation. For making KIKO3D faster, it is important to apply an effective method for the solution of the large sparse inhomogeneous equation in a time step when solving the time-dependent nodal kinetic equations. For this purpose, a variant of the generalized minimal residual (GMRES) method was used first. Later, we have found that the more recent method bi-conjugate gradient stabilized (Bi-CGSTAB) works more effectively. Validation of the improved code has been Performed by solving of a VVER-1000 kinetic benchmark problem. The results obtained by the old GMRES and new Bi-CGSTAB methods are compared.