Modified Block Newton iteration for the lambda modes problem in hexagonal geometry

To study the behavior of nuclear reactors like the Russian VVER reactors it is necessary to solve the time dependent neutron diffusion equation using a hexagonal mesh. This problem can be solved by means of a modal method, which uses a set of dominant modes to expand the neutron flux. To obtain this set of modes a differential eigenvalue problem for a steady state has to be solved. The spatial part of the equations is discretized using a high order finite element method, based on the fact that the neutron flux can be expanded in terms of the modified Dubiner´s polynomials. For the transient calculations using the modal method with a moderate number of modes, these modes must be updated each time step to maintain the accuracy of the solution. A Modified Block Newton iteration is studied to update the modes. The performance of the method has been tested for a hypothetical transient in a 2-dimensional VVER 440 reactor.