Spectral-Nodal Deterministic Methodology for Neutron Shielding Calculations using the X, Y - geometry Multigroup Transport Equation in the Discrete Ordinates Formulation

In this work, we present the most recent numerical results in a nodal approach, which resulted in the development of a new numerical spectral nodal method, based on the spectral analysis of the multigroup, isotropic scattering neutron transport equations in the discrete ordinates ($S_N$) formulation for fixed-source calculations in non-multiplying media (shielding problems). The numerical results refer to simulations of typical problems from the reactor physics field, in rectangular two-dimensional Cartesian geometry, $X, Y$ geometry, and are compared with the traditional Diamond Difference ($DD$) fine-mesh method results, used as a reference, and the spectral coarse-mesh method Green's function ($SGF$) results.

Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive.

A MULTIPHYSICS SIMULATION SUITE FOR SODIUM COOLED FAST REACTORS

A simulation suite has been developed to model reactor power distribution and multiphysics feedback effects in Sodium-cooled Fast Reactors (SFRs). This suite is based on the Finite Element Method (FEM) and employs a general, unstructured mesh to solve the Simplified P3 (SP3) neutron transport equations. In the FEM implementation, two-dimensional triangular elements and three-dimensional wedge elements are selected. Wedge elements are selected for their natural description of hexagonal geometry common to fast reactors. Thermal feedback effects within fast reactors are modeled within the simulation suite. A thermal hydraulic model is developed, modeling both axial heat convection and radial heat conduction within fuel assemblies. A thermal expansion model is included and is demonstrated to significantly affect reactivity. This simulation suite has been employed to model the Advanced Burner Reactor (ABR) benchmark, specifically the MET-1000. It has been demonstrated that these models sufficiently describe the multiphysics feedback phenomena and can be used to estimate multiphysics reactivity feedback coefficients.

DEMONSTRATION OF A LINEAR PROLONGATION CMFD METHOD ON MOC

Coarse Mesh Finite Difference (CMFD) method is a very effective method to accelerate the iterations for neutron transport calculation. But it can degrade and even fail when the optical thickness of the mesh becomes large. Therefore several methods, including partial current-based CMFD (pCMFD) and optimally diffusive CMFD (odCMFD), have been proposed to stabilize the conventional CMFD method. Recently, a category of “higherorder” prolongation CMFD (hpCMFD) methods was proposed to use both the local and neighboring coarse mesh fluxes to update the fine cell flux, which can solve the fine cell scalar flux discontinuity problem between the fine cells at the bounary of the coarse mesh. One of the hpCMFD methods, refered as lpCMFD, was proposed to use a linear prolongation to update the fine cell scalar fluxes. Method of Characteristics (MOC) is a very popular method to solve neutron transport equations. In this paper, lpCMFD is applied on the MOC code MPACT for a variety of fine meshes. A track-based centroids calculation method is introduced to find the centroids coordinates for random shapes of fine cells. And the numerical results of a 2D C5G7 problem are provided to demonstrate the stability and efficiency of lpCMFD method on MOC. It shows that lpCMFD can stabilize the CMFD iterations in MOC method effectively and lpCMFD method performs better than odCMFD on reducing the outer MOC iterations.

Some Compactness and Interpolation Results for Linear Boltzmann Equation

We discuss some compactness results inLp (1≤p<∞)spaces related to the spectral theory of neutron transport equations for general classes of collision operators and Radon measures having velocity spaces as supports covering most physical models. We show in particular that the asymptotic spectrum of the transport operator is independent ofp.

Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media

We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.