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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

Towne, Charles E.↗
DOE OSTI2019

Extension and Demonstration of NEAMS Multiphysics Tools to Lead-Cooled, Sodium-Cooled, and Molten Salt Fast Reactor Applications

The SHARP toolkit is a high-fidelity reactor simulation tool developed under the U.S. Department of Energy, Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign. SHARP toolkit is comprised of the neutronics module PROTEUS thermal hydraulics module Nek5000, and structural mechanics module Diablo. During FY17 and FY18, the PROTEUS and Nek5000 components of SHARP were applied to solve challenging sodium-cooled fast reactor (SFR) problems. In particular, selected hot channel factors (HCF) for a prototype metal-fueled SFR design (the AFR-100) were analyzed in high fidelity, and the “SHARP zooming capability” for SFRs was developed and demonstrated to reduce computational expense for full core problems in cases where detailed data is needed in selected fuel assemblies. After the previous success applying SHARP to challenging SFR problems, the focus in FY19 expanded to additional fast reactor applications: lead cooled fast reactors (LFR), sodium cooled fast reactors (SFR), and fast molten salt reactors (MSR). The specific technical tasks were (1) assessment of hot channel factors for LFR, for which no data currently exists, (2) implementation of a gamma transport capability in the PROTEUS solvers to extend the zooming capability to non-fueled assemblies, (3) demonstration of zooming capability in assemblies of the Versatile Test Reactor (VTR), and (4) development of a new coupled capability for simulating fast MSRs, specifically modeling precursor transport inside and outside the core. The progress on tasks (1) and (3) are discussed primarily in this document. Tasks (2) and (4) are briefly mentioned in this document, and the interested reader is referred to separate reports for detailed information. First-of-a-kind hot channel factor (HCF) estimation for LFR with high fidelity codes (PROTEUS/Nek5000) was successfully demonstrated in this study. Selected HCF were computed and compared with SFR data (AFR-100, EBR-II). The findings confirm that different reactor types, design parameters and uncertainties lead to different HCFs. Careful estimation of HCF for a specific design is necessary to obtain appropriate HCFs. In addition to improvement in HCF accuracy, high fidelity tools generate data to help the designer better understand the mechanism of the impact from these uncertainties. For example, the impact of cladding thickness manufacturing tolerance resulted in non-intuitive effects in the corner pins of the LFR assembly. This procedure of computing HCF using high fidelity models shows promise and flexibility for being repeated for any arbitrary reactor of choice, since these tools are targeted to solve many reactor types and geometries. Progress was made towards extending the previously demonstrated SHARP zooming capability to non-fueled SFR assemblies. In particular, a gamma transport capability was implemented in both high fidelity PROTEUS solvers in order to accurately account for heat deposition caused by gamma particles, which accounts for ~10% of total core power. Neutronics verification cases were carried out for a candidate Versatile Test Reactor (VTR) design using the new gamma transport capability in PROTEUS. Comparisons were made with continuous energy MCNP calculations and shown to agree well. The models for the full core design with heterogeneous control and fuel assemblies is in progress and will be completed in FY20. In the fast molten salt reactor (MSR) domain, a new capability was developed to model the flow of neutron precursors both inside and outside of the core, which impacts the effective delayed neutron fraction of the system. The PROTEUS-SN and PROTEUS-NODAL solvers were coupled to Nek5000 in order to simulate precursor flow. The workflows were demonstrated on test problems. The fast MSR modeling capability was supported under two other work packages, and comprehensive details are included in a separate report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Warthog: Coupling Status Update

The Warthog code was developed to couple codes that are developed in both the Multi-Physics Object-Oriented Simulation Environment (MOOSE) from Idaho National Laboratory (INL) and SHARP from Argonne National Laboratory (ANL). The initial phase of this work, focused on coupling the neutronics code PROTEUS with the fuel performance code BISON. The main technical challenge involves mapping the power density solution determined by PROTEUS to the fuel in BISON. This presents a challenge since PROTEUS uses the MOAB mesh format, but BISON, like all other MOOSE codes, uses the libMesh format. When coupling the different codes, one must consider that Warthog is a light-weight MOOSE-based program that uses the Data Transfer Kit (DTK) to transfer data between the various mesh types. Users set up inputs for the codes they want to run, and then Warthog transfers the data between them. Currently Warthog supports XSProc from SCALE or the Sub-Group Application Programming Interface (SGAPI) in PROTEUS for generating cross sections. It supports arbitrary geometries using PROTEUS and BISON. DTK will transfer power densities and temperatures between the codes where the domains overlap. In the past fiscal year (FY), much work has gone into demonstrating two-way coupling for simple pin cells of various materials. XSProc was used to calculate the cross sections, which were then passed to PROTEUS in an external file. PROTEUS calculates the fission/power density, and Warthog uses DTK to pass this information to BISON, where it is used as the heat source. BISON then calculates the temperature profile of the pin cell and sends it back to XSProc to obtain the temperature corrected cross sections. This process is repeated until the convergence criteria (tolerance on BISON solve, or number of time steps) is reached. Models have been constructed and run for both uranium oxide and uranium silicide fuels. These models demonstrate a clear difference in power shape that is not accounted for in a stand-alone BISON run. Future work involves improving the user interface (UI), likely through integration with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Workbench. Furthermore, automating the input creation would ease the user experience. The next priority is to continue coupling the work with other codes in the SHARP package. Efforts on other projects include work to couple the Nek5000 thermo-hydraulics code to MOOSE, but this is in the preliminary stages.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Assessment of the Griffin Reactor Multiphysics Application Using the Empire Micro Reactor Design Concept

In late 2019, INL and ANL agreed to jointly develop the reactor physics code named Griffin based on the integration of the two code suites, MAMMOTH/Rattlesnake (INL) and MC2 - 3/PROTEUS (ANL). Griffin is being developed based on the MOOSE framework and MOOSE quality assurance procedures. This decision was made to be able to allow DOE-NE to efficiently invest funding to this area and to provide effective and timely support for existing and potential users; the latter includes industry and government organizations who are developing various types of advanced reactors in the near and long term. Since MAMMOTH/Rattlesnake has been developed based on the MOOSE framework, the INL/ANL Griffin development team agreed to build Griffin beginning with a merger of MAMMOTH and Rattlesnake into a single code and moving forward by implementing capabilities from the PROTEUS suite into Griffin. Moving forward, both ANL and INL efforts are equally invested in the Griffin project, with management support, to provide an advanced reactor multiphysics tool to assist in reactor design, optimization, and safety analysis. Much work remains in moving Griffin forward to migrate PROTEUS capabilities and to optimize performance to meet user needs. The main objective of this work is to assess the current status of Griffin capabilities in terms of performance and accuracy, to determine priorities for PROTEUS migration, and to identify capabilities and features to improve for supporting the code integration effort. For this assessment, the Empire micro reactor problem that was developed in the ARPA-E MEITNER program was selected as an advance reactor concept of interest to the technical community. The Empire reactor problem was expanded from its original incomplete specification to be a small heat-pipe-cooled micro reactor core with ~113 cm radius and 70 cm in height, composed of 18 fuel assemblies, 12 control drums, and beryllium radial and axial reflectors. In the current model, using 5 cm axial reflectors specified in the original Empire assembly model, more than 10% of neutrons leak axially and through the empty center safety hole, as well as through heat pipe channels in fuel assembly elements that extend through the top reflector region. Several calculation models of the core were defined for systematic assessment, including 2-D and 3-D fuel assemblies and whole cores with cylindrical boundaries. Cross sections were generated using Serpent 2, and meshes were produced using the Argonne mesh tool or the INL neutronics meshing tools combined with CUBIT. Cross sections and meshes were converted to the ISOXML and Exodus formats, respectively, so that Griffin and PROTEUS could use consistent data for solving the reactor problems. With the prepared cross sections and meshes, PROTEUS was run first to ensure that all input data were correctly generated and input options in terms of angle, mesh, and energy group were accurately determined. Comparisons against Serpent 2 solutions were made in terms of eigenvalue and pin power. The same calculations and comparisons were then conducted using Griffin. For the fuel assembly and whole core problems, the PROTEUS eigenvalues agreed well with reference Serpent 2 solutions within 100 and 30 pcm, respectively, and pin power differences relative to Serpent 2 were overall less than 2.2% and RMS 0.8% for the whole core models. This indicated that all input data were properly prepared. Using the same data, Griffin was run selecting the SAAF-CFEM SN solver with Legendre-Gaussian quadrature and NDA and DSA for acceleration. It was found that the SAAF-CFEM solver of Griffin required finer meshes to achieve eigenvalue and pin power solutions in good agreement with Serpent 2, consequently requiring more memory requirement and longer computation time. On the other hand, the SPH-Diffusion 2-D core calculations performed using Griffin were able to recover the exact eigenvalue from the reference Serpent 2 solutions, resulting in a pin-power distribution with an RMS of 0.6% and maximum absolute difference of less than 1.4%. The runtimes for SPH-Diffusion for the 2-D core were less than 3 minutes on 40 cores. During this evolution of this evaluation, many updates were made in Griffin by the Griffin development team of INL (focusing on software updates) and ANL (reviewing and supporting software updates) to complete this assessment. Observations from the code assessment are presented in the conclusion section of this report, followed by a discussion of recommendations for future work.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Initial Comparison of Direct and Legacy Modeling Approaches for Radial Core Expansion Analysis

Radial core expansion in sodium-cooled fast reactors provides an important reactivity feedback effect. As the reactor power increases due to normal start up conditions or accident scenarios, the core and surrounding materials heat up, causing both grid plate expansion and bowing of the assembly ducts. When the core restraint system is designed correctly, the resulting structural deformations introduce negative reactivity which decreases the reactor power. Historically, an indirect procedure has been used to estimate the reactivity feedback due to structural deformation which relies upon perturbation theory and coupling legacy physics codes with limited geometry capabilities. With advancements in modeling and simulation, radial core expansion phenomena can now be modeled directly, providing an assessment of the accuracy of the reactivity feedback coefficients generated by indirect legacy methods. Recently a new capability was added to the PROTEUS-SN unstructured geometry neutron transport solver to analyze deformed meshes quickly and directly. By supplying the deformed mesh in addition to the base configuration input files, PROTEUS-SN automatically processes material adjustments including calculation of region densities to conserve mass, calculation of isotopic densities according to material models (for example, sodium density as a function of temperature), and subsequent re-homogenization of materials. To verify the new capability of directly simulating deformed meshes, PROTEUS-SN was used to compute reactivity feedback for a series of contrived yet representative deformed configurations for the Advanced Burner Test Reactor design. The indirect legacy procedure was also performed to generate reactivity feedback coefficients for the same deformed configurations. Interestingly, the legacy procedure consistently overestimated reactivity feedbacks by 35% compared to direct simulations by PROTEUS-SN. This overestimation indicates that the legacy procedures are in fact not conservative and could be overestimating reactivity feedback effects that are closely tied to reactor safety. We conclude that there is indeed value in performing direct simulation of deformed meshes despite the increased computational expense. PROTEUS-SN is already part of the SHARP multi-physics toolkit where both thermal hydraulics and structural mechanical feedback modeling can be applied but this is the first comparison of direct simulation to legacy techniques for radial core expansion.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

FY16 Status Report on NEAMS Neutronics Activities

The goal of the NEAMS neutronics effort is to develop a neutronics toolkit for use on sodium-cooled fast reactors (SFRs) which can be extended to other reactor types. The neutronics toolkit includes the high-fidelity deterministic neutron transport code PROTEUS and many supporting tools such as a cross section generation code MC 2 -3, a cross section library generation code, alternative cross section generation tools, mesh generation and conversion utilities, and an automated regression test tool. The FY16 effort for NEAMS neutronics focused on supporting the release of the SHARP toolkit and existing and new users, continuing to develop PROTEUS functions necessary for performance improvement as well as the SHARP release, verifying PROTEUS against available existing benchmark problems, and developing new benchmark problems as needed. The FY16 research effort was focused on further updates of PROTEUS-SN and PROTEUS-MOCEX and cross section generation capabilities as needed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

FY17 Status Report on NEAMS Neutronics Activities

Under the U.S. DOE NEAMS program, the high-fidelity neutronics code system has been developed to support the multiphysics modeling and simulation capability named SHARP. The neutronics code system includes the high-fidelity neutronics code PROTEUS, the cross section library and preprocessing tools, the multigroup cross section generation code MC2-3, the in-house meshing generation tool, the perturbation and sensitivity analysis code PERSENT, and post-processing tools. The main objectives of the NEAMS neutronics activities in FY17 are to continue development of an advanced nodal solver in PROTEUS for use in nuclear reactor design and analysis projects, implement a simplified sub-channel based thermal-hydraulic (T/H) capability into PROTEUS to efficiently compute the thermal feedback, improve the performance of PROTEUS-MOCEX using numerical acceleration and code optimization, improve the cross section generation tools including MC2-3, and continue to perform verification and validation tests for PROTEUS.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Demonstration of NEAMS Multiphysics Tools for Fast Reactor Applications

The SHARP toolkit is a high-fidelity reactor simulation tool developed under the U.S. Department of Energy, Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign. SHARP toolkit is comprised of the neutronics module PROTEUS thermal hydraulics module Nek5000, and structural mechanics module Diablo. During FY17 and FY18, the PROTEUS and Nek5000 components of SHARP were applied to solve challenging sodium-cooled fast reactor (SFR) problems. In particular, selected hot channel factors (HCF) for a prototype metal-fueled SFR design (the AFR-100) were analyzed in high fidelity, and the “SHARP zooming capability” for SFRs was developed and demonstrated to reduce computational expense for full core problems in cases where detailed data is needed in selected fuel assemblies. After the previous success applying SHARP to challenging SFR problems, the focus in FY19 and FY20 expanded to additional fast reactor applications including lead cooled fast reactors (LFR) and sodium cooled fast reactors (SFR). The specific technical tasks were (1) assessment of hot channel factors for LFR, for which no data currently exists, and (2) demonstration of zooming capability in assemblies of the Versatile Test Reactor (VTR). First-of-a-kind hot channel factor (HCF) estimation for LFR with high fidelity codes (PROTEUS/Nek5000) was successfully demonstrated in this study which began in FY19 and continued in FY20. Selected HCF were computed and compared with SFR data (AFR-100, EBR-II). The findings confirm that different reactor types, design parameters and uncertainties lead to different HCFs. Careful estimation of HCF for a specific design is necessary to obtain appropriate HCFs. In addition to improvement in HCF accuracy, high fidelity tools generate data to help the designer better understand the mechanism of the impact from these uncertainties. For example, the impact of cladding thickness manufacturing tolerance resulted in non-intuitive effects in the corner pins of the LFR assembly. This procedure of computing HCF using high fidelity models shows promise and flexibility for being repeated for any arbitrary reactor of choice. Along with the application on SFR and LFR, the capability of the tools has also been matured to deal with different reactor types and designs. Progress was made towards extending the previously demonstrated SHARP zooming capability to non-fueled SFR assemblies. In particular, in FY19 a gamma transport capability was implemented in both high fidelity PROTEUS solvers in order to accurately account for heat deposition caused by gamma particles, which accounts for ~10% of total core power. Neutronics verification cases were carried out for a candidate Versatile Test Reactor (VTR) design using the new gamma transport capability in PROTEUS. Comparisons were made with continuous energy MCNP calculations and shown to agree well. The models for the full core design with heterogeneous control and fuel assemblies is in progress for PROTEUS-SN and completed with MCNP. The MCNP power distributions were transferred to Nek5000 to perform thermal hydraulic calculations of the control and fuel assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2006

Cooperative Collision Avoidance Step 1 - Technology Demonstration Flight Test Report. Revision 1

The National Aeronautics and Space Administration (NASA) Access 5 Project Office sponsored a cooperative collision avoidance flight demonstration program for unmanned aircraft systems (UAS). This flight test was accomplished between September 21st and September 27th 2005 from the Mojave Airport, Mojave, California. The objective of these flights was to collect data for the Access 5 Cooperative Collision Avoidance (CCA) Work Package simulation effort, i.e., to gather data under select conditions to allow validation of the CCA simulation. Subsequent simulation to be verified were: Demonstrate the ability to detect cooperative traffic and provide situational awareness to the ROA pilot; Demonstrate the ability to track the detected cooperative traffic and provide position information to the ROA pilot; Demonstrate the ability to determine collision potential with detected cooperative traffic and provide notification to the ROA pilot; Demonstrate that the CCA subsystem provides information in sufficient time for the ROA pilot to initiate an evasive maneuver to avoid collision; Demonstrate an evasive maneuver that avoids collision with the threat aircraft; and lastly, Demonstrate the ability to assess the adequacy of the maneuver and determine that the collision potential has been avoided. The Scaled Composites, LLC Proteus Optionally Piloted Vehicle (OPV) was chosen as the test platform. Proteus was manned by two on-board pilots but was also capable of being controlled from an Air Vehicle Control Station (AVCS) located on the ground. For this demonstration, Proteus was equipped with cooperative collision sensors and the required hardware and software to place the data on the downlink. Prior to the flight phase, a detailed set of flight test scenarios were developed to address the flight test objectives. Two cooperative collision avoidance sensors were utilized for detecting aircraft in the evaluation: Traffic Alert and Collision Avoidance System-II (TCAS-II) and Automatic Dependent Surveillance Broadcast (ADS-B). A single intruder aircraft was used during all the flight testing, a NASA Gulfstream III (G-III). During the course of the testing, six geometrically different near-collision scenarios were evaluated. These six scenarios were each tested using various combinations of sensors and collision avoidance software. Of the 54 planned test points 49 were accomplished successfully. Proteus flew a total of 21.5 hours during the testing and the G-III flew 19.8 hours. The testing fully achieved all flight test objectives. The Flight IPT performed an analysis to determine the accuracy of the simulation model used to predict the location of the host aircraft downstream during an avoidance maneuver. The data collected by this flight program was delivered to the Access 5 Cooperative Collision Avoidance (CCA) Work Package Team who was responsible for reporting on their analysis of this flight data.

Trongale, Nicholas A.↗
NASA NTRS2004

Status of a UAV SAR Designed for Repeat Pass Interferometry for Deformation Measurements

Under the NASA ESTO sponsored Instrument Incubator Program we have designed a lightweight, reconfigurable polarimetric L-band SAR designed for repeat pass deformation measurements of rapidly deforming surfaces of geophysical interest such as volcanoes or earthquakes. This radar will be installed on an unmanned airborne vehicle (UAV) or a lightweight, high-altitude, and long endurance platform such as the Proteus. After a study of suitable available platforms we selected the Proteus for initial development and testing of the system. We want to control the repeat track capability of the aircraft to be within a 10 m tube to support the repeat deformation capability. We conducted tests with the Proteus using real-time GPS with sub-meter accuracy to see if pilots could fly the aircraft within the desired tube. Our results show that pilots are unable to fly the aircraft with the desired accuracy and therefore an augmented autopilot will be required to meet these objectives. Based on the Proteus flying altitude of 13.7 km (45,000 ft), we are designing a fully polarimetric L-band radar with 80 MHz bandwidth and 16 km range swath. This radar will have an active electronic beam steering antenna to achieve Doppler centroid stability that is necessary for repeat-pass interferometry (RPI). This paper will present are design criteria, current design and expected science applications.

radar↗
DOE OSTI2014

Enhancements to the SHARP Build System and NEK5000 Coupling

The SHARP project for the Department of Energy's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program provides a multiphysics framework for coupled simulations of advanced nuclear reactor designs. It provides an overall coupling environment that utilizes custom interfaces to couple existing physics codes through a common spatial decomposition and unique solution transfer component. As of this writing, SHARP couples neutronics, thermal hydraulics, and structural mechanics using PROTEUS, Nek5000, and Diablo respectively. This report details two primary SHARP improvements regarding the Nek5000 and Diablo individual physics codes: (1) an improved Nek5000 coupling interface that lets SHARP achieve a vast increase in overall solution accuracy by manipulating the structure of the internal Nek5000 spatial mesh, and (2) the capability to seamlessly couple structural mechanics calculations into the framework through improvements to the SHARP build system. The Nek5000 coupling interface now uses a barycentric Lagrange interpolation method that takes the vertex-based power and density computed from the PROTEUS neutronics solver and maps it to the user-specified, general-order Nek5000 spectral element mesh. Before this work, SHARP handled this vertex-based solution transfer in an averaging-based manner. SHARP users can now achieve higher levels of accuracy by specifying any arbitrary Nek5000 spectral mesh order. This improvement takes the average percentage error between the PROTEUS power solution and the Nek5000 interpolated result down drastically from over 23 % to just above 2 %, and maintains the correct power profile. We have integrated Diablo into the SHARP build system to facilitate the future coupling of structural mechanics calculations into SHARP. Previously, simulations involving Diablo were done in an iterative manner, requiring a large amount manual work, and left only as a task for advanced users. This report will detail a new Diablo build system that was implemented using GNU Autotools, mirroring much of the current SHARP build system, and easing the use of structural mechanics calculations for end-users of the SHARP multiphysics framework. It lets users easily build and use Diablo as a stand-alone simulation, as well as fully couple with the other SHARP physics modules. The top-level SHARP build system was modified to allow Diablo to hook in directly. New dependency handlers were implemented to let SHARP users easily build the framework with these new simulation capabilities. The remainder of this report will describe this work in full, with a detailed discussion of the overall design philosophy of SHARP, the new solution interpolation method introduced, and the Diablo integration work. We will conclude with a discussion of possible future SHARP improvements that will serve to increase solution accuracy and framework capability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Status Report on NEAMS PROTEUS/ORIGEN Integration

The US Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program has contributed significantly to the development of the PROTEUS neutron transport code at Argonne National Laboratory and to the Oak Ridge Isotope Generation and Depletion Code (ORIGEN) depletion/decay code at Oak Ridge National Laboratory. PROTEUS’s key capability is the efficient and scalable (up to hundreds of thousands of cores) neutron transport solver on general, unstructured, three-dimensional finite-element-type meshes. The scalability and mesh generality enable the transfer of neutron and power distributions to other codes in the NEAMS toolkit for advanced multiphysics analysis. Recently, ORIGEN has received considerable modernization to provide the high-performance depletion/decay capability within the NEAMS toolkit. This work presents a description of the initial integration of ORIGEN in PROTEUS, mainly performed during FY 2015, with minor updates in FY 2016.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Development of a Novel Accelerator for Neutron Transport Solution Using the Galerkin Spectral Element Methods (Final Report)

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to develop and implement advanced acceleration schemes for the DOE NEAMS neutronics code PROTEUSSN. The project team included the University of Massachusetts Lowell, The Ohio State University, University of Michigan, and Argonne National Laboratory. The PROTEUS code is a high-fidelity capable deterministic neutron transport code based on unstructured finite element meshes, which solves the steady-state and transient neutron transport problem using the 2nd-order discrete ordinate method (SN2ND), the method of characteristics (MOC), and the advanced nodal transport method (NODAL). The DSA scheme has been implemented in PROTEUS to speed up SN transport calculations. The existing DSA scheme employs a consistent finite element formulation on the same fine mesh structure as the SN solution While the use of consistent discretizations makes the DSA method effective, it does not necessarily make it efficient because the numerical solution of a discretized elliptic diffusion problem itself can be costly, particularly when the problem size becomes large. We developed a new discontinuous Galerkin (DG) discretization of the diffusion equation, called DG-DSA, which can effectively and efficiently accelerate the SN transport iterations. As compared with the previous work, the novelty of our method is that the diffusion equation is solved on a coarse-mesh grid using the DG methods, and the DG diffusion discretization incorporates local hp adaptation, i.e., local adaptation of mesh size and/or polynomial degree, based on local total cross section (or optical thickness). Therefore, the resulting number of degrees of freedom (DOF) of the DG discretization is much less than the conventional consistent DSA discretizations, and thus DG-DSA can achieve significant improvement in computational efficiency. We implemented this scheme in PROTEUS-SN. In addition, we developed a new stabilization scheme named linear prolongation CMFD (lpCMFD). A novel feature of this scheme is that the conventional flat flux ratio–based scaling approach is replaced with a linear interpolation of the scalar flux differences at the coarse-mesh cell edges between the neutron transport and CMFD calculations. Fourier convergence analysis and numerical results show that lpCMFD is unconditionally stable and more effective than other CMFD based on acceleration schemes such as pCMFD, odCMFD. We also developed a new nonlinear diffusion acceleration scheme for solving neutron transport equations. This scheme, called LR-NDA, employs a local refinement approach on the framework of CMFD by solving a local boundary value problem of the scalar flux on the coarse-mesh structure to replace the piecewise constant scalar flux obtained by CMFD. The refined flux is then used to update the scalar flux in the neutron transport source iteration. It has been demonstrated that that LR-NDA is much more effective and stable than CMFD for a wide range of optical thicknesses. LR-NDA is a local adaptive method, which means LR-NDA does not necessarily require local refinement for all the coarse-mesh cells on the problem domain, i.e., it can be used only for relatively optically thick regions where the standard CMFD scheme would encounter the convergence problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗