Verification and Validation of High-Order Short-Characteristics-Based Deterministic Transport Methodology on Unstructured Grids, Reactor Concepts RD-D.

摘要

THOR is a radiation transport code that solves the steady-state, multigroup, discrete ordinates approximation of the linear Boltzmann equation in three-dimensional geometry on unstructured tetrahedral cells. The spatial approximation implemented in THOR is the Arbitrarily High Order Transport method of the Characteristic type, AHOTC, extended to Unstructured Grids, AHOTC-UG. The tasks of this project were designed to raise the production level of THOR by supplementing its capabilities then conducting a comprehensive Verification and Validation (V&V) exercise based on Idaho National Laboratory's (INL) Advanced Test Reactor (ATR) configuration and measured data. The primary development work on the code commenced with a study of numerical stability of the underlying equations in the optically-thin cell limit that revealed the cause for the structural instability observed in earlier results. Basically the recursive algorithm used in evaluating the flux spatial moments in terms of lower-order moments accumulated the error to unacceptable magnitude for higher orders. This deficiency was addressed by reformulating the equations and subsequent solution algorithm into a non-recursive form that was found to be numerically stable with increasing spatial expansion order. Additionally we examined the numerical stability of the spatial weights associated with AHOTC-UG and constructed asymptotic expansions that are resilient in the optically thin and thick cell regimes. Many improvements intended to enhance THORs robustness and computational efficiency were implemented, including a cycle-breaking algorithm that may be necessary in some complex automatically-generated unstructured grids.