Nonlinear nodal expansion and finite difference schemes for the neutron diffusion equation

Two nonlinear iteration methods based on a onenode nodal expansion (NE) and a twonode finite difference method (FD) were developed to accurately and quickly solve the multidimensional, multigroup neutron diffusion equation. The two methods were compared with the nonlinear iteration method based on a twonode nodal expanion. The interface neutron currents were calculated using either the onenode nodal expanion or the twonode finite difference technique and then the nonlinear coefficients at the interface were updated. The coarse mesh finite difference equations were then solved using the updated nonlinear coefficients. Benchmark calculations showed that the nonlinear iteration method based a one or twonode nodal expansion was considerably faster than the nodal Green's function method with nearly the same accuracy. The nonlinear finite difference method has almost the same speed and accurcy as the Green's function method and the accuracy of the finite difference method can be conveniently increased by using more subnodes.