A Novel Tool for the Assessment and Validation of Acceleration Methods for Solving the Neutron Transport Equation

The Boltzmann Transport Equation describes the behavior of the population of neutronsin nuclear systems. Solving this equation is therefore of great interest to researchers designing future generations of nuclear reactors among many other applications. Solving the neutron transport equation using computers requires careful discretization of the phase space and iterative methods to converge to a solution. These methods can be slow to converge, often due to material properties in systems of interest. Highly scattering media, for example, are often used in reactor designs and can cause many methods to take arbitrarily long to converge. To combat computational inefficiencies, researchers modify the iteration schemes using a broad class of algorithms called acceleration methods. Implementing, assessing, and validating acceleration methods is necessary but challenging for researchers. A particular challenge is confirming whether an acceleration method is actually improving the simulation the way we expect. Computational tools are generally designed for solving the problem of interest, not for assessing the solving process itself. We present the Bay Area Radiation Transport (BART) code, a computational tool designed with the researcher as the end-user in mind. This code is designed to relieve some of the burden of implementing novel acceleration methods. It leverages modern coding practices to minimize the amount of code that must be modified to implement new methods and aims to make clear where these modifications need to be made. This both simplifies implementation and makes comparison across methods easier. Once implemented, the code provides a high-quality environment for testing the new method. The design of the code isolates modifications, providing a good comparison to a base case as well as other acceleration methods. Making this comparison is supported by the inclusion of a robust instrumentation system. Developers are empowered to collect and extract data of any type from anywhere in the solving process with ease. This data collection can then be used to assess and validate implemented methods. Importantly, these data can interrogate whether the problems are being accelerated where and how the methods are designed to provide acceleration. Typically, 2 developers do not have the ability to see if a method is actually doing what we think, we only measure compute time and iteration count; BART provides much more information about what is happening. Finally, the code is designed with comprehensive testing to provide a reproducible and trusted environment to researchers. The code itself is robust, with the ability to solve angular and scalar formulations of the transport equation in one, two, and three dimensions. We demonstrate a level-symmetric- like Gaussian quadrature implemented for solving angular formulations and show that it accurately integrates the spherical harmonics. We present two acceleration methods, the two-grid (TG) and nonlinear diffusion acceleration (NDA) methods. The TG method is designed to accelerate the Gauss-Seidel (GS) iteration process in the presence of large amounts of upscattering. We demonstrate the effectiveness of the method using the BART code in one, two, and three dimensions. The effectiveness is shown by a reduction in total GS iterations by a larger factor than is required for the method to be efficient. We also demonstrate the benefits of the BART code, showing more rapid convergence of the scattering source using the code’s unique instrumentation. The NDA method is designed to accelerate convergence by converging diffusive error modes more rapidly. We demonstrate effectiveness by reducing total iterations in one, and three dimensions. For the one-dimensional case, we demonstrate a significant reduction in the diffusive error modes using the BART Fourier analysis instrumentation. We will examine the goals of the BART code and how the design meets these goals. By examining two acceleration methods and analyzing them using the data we can collect using this new tool, we will show the benefits of this novel code to the broader research community. The BART code changes how people are able to implement, assess, and validate acceleration methods. The ease of use and new information enables the development of new and better methods so we can design and build better nuclear systems.

Advisor: Slaybaugh, Rachel