CODES

'J. I. Yoon and H. G. Joo, Two-Level Coarse Mesh Finite Difference Formulation with Multigroup Source Expansion Nodal Kernels, Journal of Nuclear Science and Technology, Vol.45, No.7, p.668-682, 2008.

RENUS is a three-dimensional reactor numerical simulator that solves the time-dependent, multi-group neutron diffusion equation in the rectangular geometry. The neutronics solver employed in RENUS is the two-level coarse mesh finite difference (CMFD) formulation base on the two-node source expansion nodal method (SENM) for accurate resolution of coupling between adjacent nodes.

The source expansion nodal method (SENM) employed in RENUS is to expand the analytic form of the source appearing in the group-wise neutron diffusion equation with a set of orthogonal polynomials in order to obtain a group decoupled analytic solution. For the acceleration, a two-level CMFD scheme is established employing a multi-group and two-group CMFD. The 2G CMFD formulated by collapsing MG CMFD accelerates the MG calculation employing the efficient two-group solution methods such as the Wielandt eigenvalue shift method and the simultaneous group solution scheme (as opposed to the group-wise solution scheme). The calculation flow of the RENUS nodal solver is shown below.

A pin power reconstruction method that is readily applicable to multi-group problems with superior accuracy is employed for applications involving rectangular fuel assemblies. It employs a two-dimensional (2D), fourth order Legendre expansion of the source distribution that naturally leads to a group-decoupled, 2D semi-analytic solution of the neutron diffusion equation. The four surface average currents and four corner fluxes are used as the boundary condition to uniquely specify the homogenous solution. The corner fluxes and source expansion coefficients are iteratively determined using the condition of corner point balance and the orthogonal property of the Legendre functions. Corner discontinuity is incorporated in the calculation of the corner fluxes which turns out to be very effective in the cases of enrichment zoning.

In RENUS, a simplified T/H solution method which solves the radial heat conduction and axial heat convection problems is employed for a closed pin channel configuration. Here a one-dimensional single-phase flow model is employed under the assumption of constant pressure to determine the axial coolant temperature and density distribution. The radial fuel temperature distribution is obtained by using an FDM solver which is to solve the radial heat conduction equation. Both the steady-state and transient versions of the T/H solver are available.

For the kinetics calculation, the CMFD transient fixed source problem is formulated based on the theta method and the second order precursor integration method. The nodal correction is performed conditionally when there is sufficient change in the reactor condition. The transient nodal equation is formed in the exactly same form as the steady-state equation by moving all the transient specific source terms to the right hand side. Therefore the SENM solver and the linear system solver used for the steady-state solution can be used with only a little additional terms for transient calculation. The conditional nodal update scheme allows very efficient transient calculation in which most of the calculation is performed in the CMFD mode by bypassing the expensive nodal calculation.

RENUS employed Triangle-based Polynomial Expansion Nodal (T-PEN) method for modeling hexagonal assemblies. This method approximates the flux distribution of triangle node as a polynomial expansion with 9 terms in two-dimension, and the hexagonal assembly constitutes of 6 triangle nodes. The hexagonal CMFD is also employed to accelerate the total computation time.