Orthogonal-Mesh, 3D Sn with Embedded 2-D Method of Characteristics for Whole-Core, Pin-Resolved Reactor Analysis

Abstract

Solutions to the Boltzmann transport equation are an important starting point for many aspects of nuclear reactor design and analysis. Many interesting physical phenomena depend on minute variations in neutron flux at scales well below the fuel pin level, requiring solutions to the transport equation that resolve this intra-pin behavior. Being large systems, direct, naive solutions to the transport equation would be impractical, even with the fastest computers available today. Solution techniques must therefore make appropriate approximations and simplifications to produce tractable yet sufficiently accurate solutions.

The Method of Characteristics (MoC) is a well-known approach to solving fine-mesh 2-D reactor problems, but has proven computationally impractical when extended directly to 3-D. Instead, a series of 2-D MoC solvers, which treat the radial dimensions, are coupled with a 1-D solver, which treats the axial dimension. This is called the 2-D/1-D method, and is the mainstay of several reactor analysis tools in use today. These methods sometimes suffer poor performance when strong axial heterogeneities are present, or when very fine axial refinement is desired. Another technique, orthogonal-mesh SN with homogenized cross sections, while efficient in 3-D, suffers poor accuracy at reasonable mesh refinements because it cannot resolve pin geometries.

This work develops a new method, called 2-D/3-D, in which 2-D MoC solvers are used to inform an orthogonal-mesh, 3-D SN solver such that accuracy is maintained on a very coarse mesh. The 2-D/3-D method uses a Corrected Diamond Difference scheme for solving the SN equations using information extracted from the 2-D MoC solvers. This preserves important streaming and collision behavior from the fine-mesh solution. A conventional differencing scheme is used to treat the axial dimension. Transverse leakage sources are used to provide axial streaming information back to the MoC solvers.

This method was applied to the three C5G7 rodded benchmark problems, and the results were compared to those of commonly-used 2-D/1-D methods. It was found that 2-D/3-D was capable of producing smaller error in most cases, at an increased memory and computational cost. These costs are likely to be minor for realistic problems and parallel decompositions.