Radiation Transport: Deterministic Approach [Slides]
Abstract not provided.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced-Order Modeling of S n Radiation Transport
Deterministic solutions to the Sn radiation transport equation can be computationally expensive to calculate. Reduced-order modeling enables efficient approximation of the full-order model (FOM) solution. We propose a novel method for constructing reduced-order models (ROMs) of the S n radiation transport equation, offline maximizing minimally invasive (OMMI) proper orthogonal decomposition (POD). POD uses the method of snapshots to create a reduced-order basis for constructing an ROM. Minimally invasive POD leverages the sweep infrastructure existing in deterministic transport codes to create a POD-based ROM, even when infeasible by traditional methods. Offline maximizing minimally invasive proper orthogonal decomposition (OMMI-POD) extends minimally invasive POD by performing sweeps offline, therefore maximizing the potential speedup. OMMI-POD does so by creating a library of reduced systems from a training set. This library of reduced systems is then interpolated to provide a rapid approximate solution of the S n radiation transport equation. The model is evaluated on a set of test problems, achieving a low error with a 466 times speedup over the FOM. Also presented is a study of the effect of sampling method on the performance of OMMI-POD, specifically comparing naive uniform sampling to the more accurate and computationally expensive greedy sampling.
97 MATHEMATICS AND COMPUTING↗
OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport
OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Performance Improvements for the Griffin Transport Solvers
Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Surface Method Raytracer
Matlab based experiments that implement multiple ray tracing methods for deterministic radiation transport, including the Surface Method as described in the PhD Thesis, "CONSERVATIVE FIRSTCOLLISION SOURCE TREATMENT FOR RAY EFFECT MITIGATION IN DISCRETE-ORDINATE RADIATION TRANSPORT SOLUTIONS" by Alex Christensen.
Christensen, AlexB↗
Griffin Software Development Plan
Griffin is a MOOSE-based reactor physics application for advanced reactor multiphysics modeling and simulation. The application is developed in a consistent multiphysics environment with strong software quality assurance. Griffin inherited most of the capabilities of MAMMOTH/Rattlesnake and is adopting the capabilities from PROTEUS that are needed in the code. The toolset includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, ad-joint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code contains the cross-section preparation capabilities applicable to fast and thermal reactors, including TRISO-fueled reactors. Core management capabilities include core performance, fuel depletion and shuffling, equilibrium core calculation, pebble-bed reactor run-in and equilibrium core, molten-salt reactor delayed neutron precursor drift, and control rod and drum movement with cusping correction. This software development plan presents the current and future capabilities and features in Griffin for the design and analysis of non-light-water reactor systems in steady-state and transient conditions.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
First-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions
Deterministic transport codes play a fundamental role in the modelling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the S method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solving them using non-traditional techniques such as ray tracing. One such code capable of doing this is Lawrence Livermore National Laboratory's deterministic transport code ARDRA. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low order of convergence and not being conservative. Therefore, a new method has been developed that traces instead to a set of points on each of a zone's surfaces and computing the currents, before using these to obtain the flux. A comparison between these two ray tracing methods showed significant advantages to the new surface method, including inherent conservation, a higher convergence rate, and an increase in calculable information like leakage. This work performed under the auspices of the U.S. Department of Energy by Lawrence Liver- more National Laboratory under Contract DE-AC52-07NA27344. (authors)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
UMT
UMT is a Sn deterministic thermal radiative transport Fortran proxy application. Its primary purpose is to research how data layout, programming paradigms and architectures effect the implementation and performance of Sn transport in Fortran on unstructured meshes. It is based on the LLNL Teton Sn deterministic thermal radiative transport code.
Yee, BenC.↗
Challenges in simulating ground interacting nuclear explosions
This paper summarizes recent above-ground nuclear explosion simulations as part of a broader effort to better characterize conditions within a fireball that may influence the chemical evolution of bomb materials and other materials entrained from the local explosion environment. A critical component of this work is validation against historic footage of atmospheric testing, requiring that we understand how the frequency-dependent sensitivity of the utilized film footage influences data captured in such images. We focus first on the early physics of a nuclear explosion in the atmosphere before discussing some of the technical challenges we seek to capture in late-time models that include more complex emplacement conditions and subsurface features. We discuss required physics packages (compressible hydrodynamics, radiation transport, as well as necessary ancillary tables such as equations of state (EOS) and opacities). Additionally, we note reasonable “shortcuts” one may make and their limitations, e.g., using ideal gas EOS, replacing spectrally resolved radiation with spectrally averaged radiation, and exchanging deterministic transport with diffusion. We then discuss an approach to achieving an equilibrated initial stress state for problems where buoyancy and subsurface lithostatic stress are important. Our methodology is presented in the context of LLNL’s ALE3D multiphysics code but may readily be implemented in other codes. In this paper, we start with a description of the challenges of NUDET simulations, followed by a presentation of the simulated intensity (flux) as it would appear on an analysis of the Dixie test. We then progressively introduce additional complexity in subsequent sections (near-surface burst and gravity initialization) before concluding.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Deterministic Particle Transport for Reducing Noise in Thermal Radiative Transfer
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Physics↗
Cost-optimized Automated Variance Reduction for Highly Angle-dependent Radiation Transport Analyses [Dissertation]
Monte Carlo variance-reduction techniques that directly bias particle direction have historically received limited attention despite being useful for many radiation transport applications such as those in which radiation travels through large regions with a low probability of colliding. One such technique is known as DXTRAN (short for deterministic transport) in the MCNP Monte Carlo radiation transport code. Until now, effectively applying DXTRAN in calculations is largely based on empirical observations of computational performance. Optimal DXTRAN parameters are identified through manual iteration. This work develops new mathematical descriptions of the DXTRAN variance-reduction process and demonstrates a new automated variance-reduction method that applies these mathematical formulations to determine the optimal application of DXTRAN in a given problem.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
SCALE Code System
The SCALE Code System is a widely used modeling and simulation suite for nuclear safety analysis and design that is developed, maintained, tested, and managed by the Reactor and Nuclear Systems Division (RNSD) of Oak Ridge National Laboratory (ORNL). SCALE provides a comprehensive, verified and validated, user-friendly tool set for criticality safety, reactor and lattice physics, radiation shielding, spent fuel and radioactive source term characterization, and sensitivity and uncertainty analysis. Since 1980, regulators, licensees, and research institutions around the world have used SCALE for safety analysis and design. SCALE provides an integrated framework with dozens of computational modules, including three deterministic and three Monte Carlo radiation transport solvers that are selected based on the desired solution strategy. SCALE includes current nuclear data libraries and problem-dependent processing tools for continuous-energy (CE) and multigroup (MG) neutronics and coupled neutron-gamma calculations, as well as activation, depletion, and decay calculations. SCALE includes unique capabilities for automated variance reduction for shielding calculations, as well as sensitivity and uncertainty analysis. SCALE’s graphical user interfaces assist with accurate system modeling, visualization of nuclear data, and convenient access to desired results.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Accelerated Deterministic Phonon Transport With Consistent Material Temperature and Intensities
Abstract We present a method for deterministically solving the frequency and temperature dependent phonon radiative transport (PRT) equation in the single-mode relaxation time (SMRT) approximation in the self-adjoint angular flux (SAAF) form. To handle the nonlinear coupling between the phonon intensities and the material temperature, we apply a linearization approach that is similar to one in thermal radiative transport. This procedure leads to the PRT equation with pseudo-scattering. The method presented includes acceleration of both the inner pseudo-scattering source iterations and outer temperature iteration with a gray diffusion synthetic acceleration (DSA) and Anderson acceleration, respectively. We use the finite-element method to discretize the PRT equation in space and the method of discrete ordinates (SN) for angular discretization. The proposed method is verified by a gray method of manufactured solutions problem and demonstrated on a problem using temperature and direction dependent multigroup data from lithium aluminate (LiAlO2). The iterative performance of the acceleration method in each test is then compared to the unaccelerated method.
Engineering↗
Moment-based adaptive time integration for thermal radiation transport
Here, in this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.
97 MATHEMATICS AND COMPUTING↗
Validation of Light Water Reactor Ex-Core Calculations with VERA
The Consortium for Advanced Simulation of Light Water Reactors (CASL) Virtual Environment for Reactor Applications (VERA) is a reactor simulation software. It offers unique capabilities by combining high-fidelity in-core radiation transport with temperature feedback by using MPACT (a deterministic neutron transport code) and COBRA-TF (a thermal-hydraulic code) with follow-on, fixed-source transport calculations using the Shift Monte Carlo code to calculate ex-core quantities of interest. In these coupled calculations, MPACT provides Shift with the fission source for follow-on ex-core calculations. These ex-core simulations can be set up to calculate detector responses, as well as the flux and fluence in ex-core regions of interest, such as the reactor pressure vessel, nozzle, and irradiated capsules. A Watts Bar Nuclear Plant Unit 1 (WBN1) ex-core model was developed, as described in this paper, and this model was used to perform coupon calculations. The results for the coupon flux calculations show close agreement with the reference values for cycle 1 produced by the two-dimensional Discrete Ordinates Transport (DORT) code and presented in a BWXT Services Inc. report. However, differences in the results (10%) seen in cycles 2 and 3 and the reasons for these differences are discussed in this paper. The VERA WBN1 model was also used to perform a vessel fluence calculation for cycle 1. Additionally, a collaboration between CASL and Duke Energy led to the first code-to-code validation of VERA for reactor ex-core applications that used a model for the Shearon Harris reactor. Results from this collaboration show excellent agreement between VERA and the Monte Carlo N-Particle Transport Code for the detector response calculations. The work performed under this collaboration is also detailed in this paper.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
235-F GoldSim Fate and Transport Model: Uncertainty Quantification
Building 235-F was configured with two missions in mind: Actinide Billet Line (ABL) and the fabrication of Pu-238 oxide for space program applications. ABL produced Np-237 billets for use in SRS reactors, whereas the design process, fabrication, and examination of Pu-238 oxide powder occurred within the following areas, respectively: Plutonium Experimental Facility (PEF), Plutonium Fuel Form (PuFF), and Old Metallography Lab (OML). By 1990 production ceased and by 2006 de-inventory occurred; however, assays have shown significant holdup remains within ABL and PuFF. As a result, 235-F is a Category 2 nuclear facility, with plans to undergo deactivation and decommission (D and D) via In-Situ Disposal (ISD). The purpose of this project is to ensure United States Environmental Protection Agency (USEPA) groundwater radiation maximum contaminant level (MCL) and dosage standards are met during the D and D of 235-F by quantifying uncertainty through probabilistic modeling and evaluation of various ISD alternatives. GoldSim is a dynamic modeling software package with a graphical, object-oriented interface capable of capturing the influence of complex system input variability on probabilistic system outcomes. A GoldSim stochastic fate and transport model for 235-F was developed and matched with a PORFLOW deterministic model to simulate probabilistic release and flow of radionuclides from ABL and PuFF into the vadose zone, the Upper Three Runs (UTR) Aquifer, and UTR Creek. The GoldSim model was used to probabilistically evaluate four ISD scenarios against USEPA groundwater radiation MCLs and dosage standards. The deterministic 235-F GoldSim fate and transport model continues to be refined to match the results of the PORFLOW deterministic model to ensure the model accurately represents radionuclide movement through the groundwater system. The stochastic variables that are utilized within the GoldSim model are founded on the most current data; a conservative perspective is taken where needed. Alignment with the PORFLOW deterministic model, coupled with input stochastic variability, allows the probabilistic 235-F GoldSim model to capture the conservative breadth of possible outcomes for radionuclide fate within this particular system. This ensures that the USEPA MCLs and dosage limits hold even in the worst case scenarios.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗