Advanced Computational Methodology for Full-Core Neutronics Calculations

Abstract

The modern computational methodology for reactor physics calculations is based on single–assembly transport calculations with reflective boundary conditions that generate homogenized few–group data, and core–level coarse-mesh diffusion calculations that evaluate a large-scale behavior of the scalar flux. Recently, an alternative approach has been developed. It is based on the low-order equations of the quasidiffusion (QD) method in order to account accurately for complicated transport effects in full–core calculations. The LOQD equations can capture transport effects to an arbitrary degree of accuracy. This approach is combined with single–assembly transport calculations that use special albedo boundary conditions which enable one to simulate efficiently effects of an unlike neighboring assembly on assembly's group data.

In this dissertation, we develop homogenization methodology based on the LOQD equations and spatially consistent coarse–mesh finite element discretization methods for the 2D low–order quasidiffusion equations for the full–core calculations. The coarse–mesh solution generated by this method preserves a number of spatial polynomial moments of the fine–mesh transport solution over coarse cells. The proposed method reproduces accurately the complicated large–scale behavior of the transport solution within assemblies. To demonstrate accuracy of the developed method, we present numerical results of calculations of test problems that simulate interaction of MOX and uranium assemblies.

We also develop a splitting method that can efficiently solve coarse-mesh discretized low-order quasidiffusion (LOQD) equations. The presented method splits the LOQD problem into two parts: (i) the $D$-problem that captures a significant part of transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation, and (ii) the $Q$-problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the $D$-problem equations are approximated by means of a finite-element method, whereas the $Q$-problem equations are discretized using a finite-volume method. Numerical results demonstrate the efficiency of the presented methodology. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the $D$-problem) to account for transport effects.