István Pataki, András Keresztúri, MTA EK, Hungary

23rd Symposium of AER on VVER Reactor Physics and Reactor Safety (2013, Štrbské Pleso, Slovakia)
Advances in spectral and core calculation methods


Two classes of nodal methods were developed with the possibility of the automated mesh
refinement leading to converged solutions. Two benchmark problems were solved for the
verification, namely the static states of AER-2 (VVER-440) and the FCM-101 (VVER-1000)
problem. From practical point of view, the differences between the converged solutions and
those from the CRONOS fine mesh solutions are negligible, nevertheless there are perceptible
deviations. Slicing only the hexagon boundaries for more continuity conditions and parallel
increase the trial functions inside the node gives better performance regarding the computer
time and accuracy than the method of subdividing the hexagon into triangles. Nevertheless,
this later method assures the possibility to take the heterogeneous structure of the node
(burnup, temperature) into account.
In spite of the increasing computing performances, coarse mesh nodal methods play an
essential role even nowadays for the tasks where the power distributions of the nuclear reactor
must be determined many times. Core design and optimization or dynamic calculations of the
safety analysis or training simulators are the most important applications in this respect. At
the same time, the accuracy requirements are more and more demanding because the margins
to be applied due to the calculation uncertainties can lead to economic burden in some cases.
These are the reasons why the nodal methods are being developed continuously for a long
time up the present days [1-5].
The KIKO3D code was developed about 15 years ago 6 and its nodal method modernization
is going on for three years in accordance with the above reasons. Meanwhile the multigroup
capability was also developed and the new code is called KIKO3DMG 7. KIKO3D and
KIKO3DMG are using a special response matrix method for solving not only the steady state
but also the time dependent diffusion equation, two specific additional response matrices are
used for that 6. These are the reasons why the methodologies found in the literature could
not be applied directly and a special development was necessary to improve the nodal
treatment. An additional standpoint of the development was that at the same time we wished
to assure the possibility of a mesh refinement up to an arbitrary deep level in order to reach
converged solutions. This later possibility proved useful for determining the uncertainty
originating just from the nodal method. Two classes of the nodal methods were developed. In
the first one the hexagonal nodes can be subdivided to arbitrary number of triangles in an
automated way while in the second one only the node boundaries are subdivided in order to
apply more and more boundary conditions and – in parallel – trial functions. In this latter case,

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