# ACMFD formulation of the HEXNEM3 method for solving the time-dependent neutron diffusion equation via modal decomposition

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28th Symposium of AER on VVER Reactor Physics and Reactor Safety (2018, Olomouc, Czechia)

[1]
Advances in spectral and core calculation methods

### Authors

Srebrin Kolev, Ivaylo Christoskov (Sofia University)

### Abstract

An ACMFD formulation of the HEXNEM3 nodal flux expansion method for solving the two-group neutron diffusion equation is developed. In the time-dependent case a modal decomposition through matrix diagonalization in the energy domain is applied in order to avoid iteration on the group sources when a fully implicit scheme in time is required. The HEXNEM3 nodal expansion model with transverse integration is applied to the modes. The ACMFD coupling coefficients are derived from the scalar flux and net current boundary and continuity conditions. The balance equations are solved simultaneously for the entire three-dimensional two-group problem. Either the node-averaged fluxes or the node-averaged modes can be chosen as nodal unknowns. The resulting nonhomogeneous linear algebraic system allows for a free choice of any appropriate stationary or non-stationary solution method. A particular advantage of the node-averaged modes balance option is that the system matrix is closer to diagonally dominant and simple preconditioning techniques can be used for convergence acceleration.