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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Application of linear prolongation to coarse mesh finite difference acceleration in CASMO5

The Coarse-Mesh Finite Difference (CMFD) method has been used for over a decade to accelerate the convergence of the Method of Characteristics (MOC) solution to the two- dimensional particle transport equation in CASMO5. Numerical testing, along with widespread use in production-level calculations, have shown that the current CMFD implementation provides stability and robustness for a wide range of realistic reactor physics problems. However, the recent development of linear prolongation has attracted attention from the community as a way to further improve the performance and stability of CMFD. Two interpolation methods for linear prolongation are presented in this work and implemented into a test version of CASMO5. The performance of the proposed interpolations, referred to as the bilinear and linear directional schemes, is evaluated in terms of runtime relative to the default constant or uniform scaling update. Numerical results indicate that the use of linear prolongation can reduce the transport solver runtime on average by approximately 10% when tested with two hundred randomly selected cases. The new directional linear interpolation, combined with default constant boundary updates, is found to provide the highest reduction in runtime for the cases analyzed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Coarse Mesh Finite Difference Acceleration for Pebble Tracking Transport in Griffin

We implemented a coarse mesh finite difference (CMFD) for accelerating transport calculations with PTT (pebble tracking transport) in the Griffin code. More specifically, extensions for transport update with the consideration of scattering operator and CMFD projection were implemented for PTT. The implementation was verified with a simplified PBR (pebble bed reactor) benchmark problem and significant performance improvements in CPU time was observed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The Legendre Polynomial Axial Expansion Method

This work presents a new formulation of the axial expansion transport method explicitly using Legendre polynomials for arbitrarily high-order expansions. This new formulation also features an alternative method of axial leakage calculation to allow for nonextruded flat source region meshes. This alternative axial leakage is introduced alongside a balance equation requirement to ensure that neutron balance is preserved in the coarse mesh for a given axial leakage formulation, which allows for effective coarse mesh finite difference acceleration. A matrix exponential table method is derived to allow for fast computations of arbitrarily high-order matrix exponentials for this work and precludes the need for further research into matrix exponential calculations for this method. Numerical results are presented that demonstrate the stability of the axial expansion method in systems with voidlike regions, showcase the speedup from matrix exponential tables, and investigate the axial convergence of the method in terms of both expansion order and mesh size.

Herring, Nicholas↗
DOE OSTI2021

Extended Applications of Subgrid Representation in the 2D/1D Method

Recent efforts in MPACT have focused on improving the performance of the 2D/1D subplane implementation to help target computational performance goals. Here, we build on previous efforts that targeted the use of subgrid treatments to improve the accuracy of control rod representation, presenting three additional applications of subgrid treatments with the goal of reducing the computational burden of simulations. These subgrid applications include treatment of spacer grids, thermal feedback, and axial reflector material representation. With these approaches, a single method of characteristics (MOC) plane can contain several different materials axially that are represented explicitly via subgrids on the coarse mesh finite difference (CMFD) mesh but are axially homogenized on the MOC mesh. This allows for a substantial reduction in the number of MOC planes needed in the calculation through the introduction of an approximate treatment, particularly with regard to the self-shielded cross sections and MOC-informed radial current coupling coefficients in CMFD. Several test problems ranging from single rod to quarter core are used to assess the solution accuracy and performance of these various subgrid representations. Overall, the accuracy of the approximations seems very reasonable, with extremely small differences in eigenvalue observed and maximum pin power errors in the 0.5% to 1.0% range. Several cases show substantial value in the compromise between accuracy and computational performance. Others highlight the new computational hurdles that future research will aim to resolve.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

MPACT Theory Manual (V.4.3)

This manual presents the theory underlying the three-dimensional (3D) whole-core, pin-resolved neutron transport calculation methodologies employed in the MPACT code. MPACT’s primary goal is to provide accurate sub-pin power distributions in a computationally efficient manner. To accomplish this, MPACT offers several different transport method options. The 2D/1D method, in which 3D problems are decomposed into an axial stack of radial “slices,” is currently the most commonly used. In this option, two-dimensional (2D) planar solutions are provided by the method of characteristics (MOC), and axial solutions are provided via one-dimensional (1D) approximate diffusion, or P3 solutions. The radial and axial solutions are coupled by (i) axial and radial transverse leakages, and (ii) a global 3D coarse mesh finite difference (CMFD) solve, which provides both acceleration and stability to the solution iteration scheme. The subsequent chapters of this manual present a range of topics, including MOC, CMFD, axial nodal transport solvers, 2D/1D, self-shielding, depletion, thermal-hydraulics, and transient methods. Development of the underlying theory of the 2D/1D method is presented, diagrams are included to highlight important algorithmic flow, and important concepts are discussed as appropriate. This manual is intended to be self-sufficient, but references to published articles and other materials are included for further reading. MPACT is a relatively new code, with new capabilities and many computational methods that did not exist until recently. This manual is an even newer document, with chapters written by several different code contributors working under time constraints. For these reasons, the manual is not yet complete and finalized. Future versions of this manual will address current deficiencies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Subplane Decusping for BWRs in MPACT

Control blade cusping can introduce significant error in boiling water reactor (BWR) calculations with MPACT when blade tips fall partway within an axial method of characteristics (MOC) plane, requiring homogenization of controlled and uncontrolled regions. This work implements subplane decusping for BWRs in MPACT by enabling BWR-compatible subplane coarse mesh finite difference (CMFD) and extending the existing decusping framework to represent between-assembly control blades that insert from the bottom of the core. The method resolves axial heterogeneity on a refined subplane mesh in the low-order solve and uses the resulting subplane flux shape to form flux-volume homogenized transport cross sections for the partially rodded MOC plane. The capability is evaluated using a single physics General Electric (GE)-14 assembly and a multiphysics Peach Bottom Unit 2 Type 1 assembly (PB2T1A) with thermal hydraulic feedback. In both cases, coarse axial meshes with and without subplane decusping are compared against fine mesh reference solutions over the full range of blade withdrawal positions. Subplane decusping reduces maximum/average eigenvalue errors from 3,369/220 pcm to 303/36 pcm for GE-14 and from 6,689/585 pcm to 1,582/109 pcm for PB2T1A. Additionally, it reduces pin power root mean square errors from 5.2%/0.8% to 1.8%/0.2% for GE-14 and from 6.9%/0.6% to 2.3%/0.1% for PB2T1A. These results demonstrate an effective, practical correction for BWR blade cusping in VERA-MPACT.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Transient Multi-Level method for Monte Carlo reactor statics calculations

The Transient Multi-Level (TML) method is applied to a time-dependent Monte Carlo transport solver to offload some of the computational burden of the expensive Monte Carlo solve to lower-order Coarse Mesh Finite Difference (CMFD) and Exact Point Kinetics Equations (EPKE) solvers via factorization of the neutron flux at the transport and CMFD levels using the Predictor Corrector Quasi-Static Method (PCQM). The Monte Carlo transient is solved by a modified fission source iteration scheme that introduces a single transient source bank. The method is implemented in the production-level Monte Carlo code, Shift, and verified with prescribed reactivity ramps from the two-dimensional version of the C5G7-TD reactor benchmark. The results show that, as compared to other quasi-static methods, the TML reduces the stochastic noise inherent to the transient Monte Carlo solver by factors of ~2 to 6 for various norm comparisons of the reactor power amplitude. Finally, the TML additionally reduces the number of Monte Carlo evaluations needed to simulate the transient, leading to roughly an order of magnitude improvement in CPU time relative to the standard PCQM for the problems tested.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Multilevel-in-Space-and-Energy CMFD in VERA

For full-core modeling in the Virtual Environment for Reactor Analysis (VERA), the three-dimensional multigroup eigenvalue neutron transport problem is solved by MPACT. To improve the efficiency of MPACT, advancements have been made in the transport accelerator. Multilevel-in-energy and multilevel-in-space coarse mesh finite difference (CMFD) solvers were developed to improve the efficiency of the CMFD accelerator. In this paper a new multilevel-in-space-and-energy CMFD solver is developed with coarsening in both space and energy on every level. Several different strategies are investigated for coarsening groups in energy. Modified V-cycle and multiple-cycle algorithms are evaluated for solving the multilevel equations. The performance of these solvers is compared for typical full-core reactor physics problems.

42 ENGINEERING↗
DOE OSTI2021

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↗
DOE OSTI2021

Hexagonal Geometries in MPACT

The MPACT code is a high-fidelity light-water reactor analysis code using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. MPACT uses the 2D/1D method to solve 3D neutron transport problems by decomposing the problem into a stack of 2D slices, each of which is solved independently using the method of characteristics (MOC). The slices are then coupled axially using the P3 nodal expansion method (NEM-P3) for the 1D axial calculations. MPACT also employs the coarse mesh finite difference (CMFD) method to accelerate calculations. This manuscript details work supporting advanced reactor designs using hexagonal pins and hexagonal assemblies such as the VVER-1000. If performed correctly, MOC is geometry agnostic. However, MPACT previously had optimizations in place for Cartesian geometries, specifically in the modularization and current calculations. Sections 2 and 3 detail the changes made to MPACT to support MOC and CMFD calculations on hexagonal geometries. Section 4 reports results demonstrating solution consistency for problems run with and without CMFD acceleration, results demonstrating solution consistency when run in serial and parallel, and pincell results using the Monte Carlo code, McCard’s benchmark results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

MPACT Software Management Plan (V.4.3)

The MPACT code solves a discretized form of the Boltzmann transport equation on a wide variety of geometries and is distributed with a multigroup neutron cross section library. MPACT provides an advanced geometrically resolved neutral-particle transport capability to solve the flux distribution throughout the entire problem geometry, and it can model the isotopic depletion, decay, and activation of materials. The flux solution in MPACT is provided using a 2D/1D synthesis method within the framework of the 3D coarse mesh finite difference (CMFD) method for which axial and radial correction factors are obtained from 2D method of characteristics (MOC) and 1D nodal expansion method (NEM), PN, or SN. Other key characteristics of the MPACT code include the subgroup method and the embedded self-shielding method (ESSM) for resonance treatment, depletion capability based on the ORIGEN exponential matrix method, and a simplified thermal-hydraulics method for temperature/fluid feedback. The sole purpose of the simplified feedback model is to provide a mechanism for testing during code development and to provide a limited capability for educational applications. Work performed at the code level supports the VERA-QA-001, quality assurance program plan (QAPP) and VERA-QA-002, VERA Software Quality Assurance Plan.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Katana

Katana is built on the pre-existing MPACT and Futility libraries. Combining those solves with several new ones that are part of Katana, nodal diffusion equations are solved in 3D using pre-tabulated nodal cross sections. 3D coarse mesh finite difference acceleration is applied to accelerate convergence. Feedback effects are accounted for during the course of the solution.

Graham, Aaron M↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗