Search NASASearch

SEARCH · Search NASA

Results for “Solution Verification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Code Verification of Multiple Physics-Fidelity Models in Hypersonic Aerodynamics

Hypersonic aerodynamics models exist across a range of physics fidelities with associated computational expenses. These models may be run independently or in a multifidelity framework that leverages their complementary strengths of speed for lower-fidelity and accuracy for higher-fidelity models. This work presents applied code verification of two lower-fidelity models contained within the Sandia hypersonic aerodynamics code. Each model has a different form that requires individualized verification approaches, including comparison to analytical solutions as well as manufactured solutions with order-of-accuracy testing. In conclusion, results of this effort include the identification and resolution of code errors and shortcomings, as well as the demonstration of code correctness and consistency for both models.

Aerodynamics

Implementation of a Drift Flux Model into SAM with Development of a Verification and Validation Test Suite for Modeling of Noncondensable Gas Mixtures

The advanced thermal-hydraulic system code, System Analysis Module (SAM), was originally developed for the modeling of single-phase flow in advanced reactors. It has since been expanded to include a four-equation drift flux model for the modeling of two-phase flows containing a noncondensable gas. The model was expanded to support the modeling of molten salt reactor (MSR) designs in which the fuel is directly dissolved in the circulating coolant. These designs have shown that circulating gas bubbles can play an important role in the management of fission products and the operational behavior of the reactor. A drift flux model was implemented to more accurately capture the localized behavior of the void in the core and its impact on the mass transfer of fission products. A thorough assessment of the new model was performed by developing a verification and validation test suite. Verification problems were designed to test all major terms in the new governing equations. The new model converged to the correct solution at the expected order of accuracy for all verification cases. The validation cases included a wide range of flow and void conditions in different pipe geometries. Although higher void experiments show a slight underprediction of void by the drift flux model, experiments that aim to reproduce Molten Salt Reactor Experiment (MSRE) experimental conditions show good agreement with the model. The gas transport model was activated for a SAM model of the MSRE to demonstrate that it can be used in a more complex model. Finally, this gas transport model will be used along with an interfacial area transport equation being implemented in SAM for the prediction of mass transport behavior in MSR conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

ML-Based Pebble Power Reconstruction for Pebble Bed Reactor Analysis

Pebble power reconstruction has been explored to complement the conventional homogenized modeling approach in pebble bed reactor (PBR) analysis, as detailed heterogeneous geometry calculations are computationally expensive. The random distribution of pebble fuels within the core challenges the application of conventional pin power reconstruction methods. To address this, we introduce a machine learning approach based on the transformer model, composed of encoder and decoder layers, to estimate the flux and power form functions for reconstructing individual pebble neutron fluxes and powers. The homogeneous neutron flux distribution within each spectral zone (SZ) is obtained from finite element solutions of global diffusion or transport calculations. Verification tests demonstrate that the trained transformer model accurately predicts power form functions over a range of conditions, including variations in pebble enrichment, location, type, SZ size, and burnup. In particular, verification using a three-dimensional PBR benchmark with burned pebbles shows good agreement in heterogeneous pebble power distributions between Griffin and Serpent. These results highlight the potential of applying conventional pin power reconstruction approaches to PBR cores with randomly distributed pebbles.

22 GENERAL STUDIES OF NUCLEAR REACTORS

The Verification and Validation of a Magnetic Plasma Fluid Model Utilizing the MOOSE (Multiphysics Object Oriented Simulation Environment) Framework

As the goal of achieving fusion power on the grid comes closer to fruition, fully coupled multiphysics models of fusion devices will be crucial. Currently, there are two main approaches to developing these platforms: (1) loosely coupled, where one couples existing codes and solvers together through input and output parameters and data, and (2) tightly coupled, where one develops the necessary models within a singular, integrated framework. This work focuses on the latter approach for magnetically confined fusion devices by developing a fluid-based plasma-edge model within the Multiphysics Object Oriented Simulation Environment (MOOSE) Framework. This effort is coordinated with other efforts to develop, test, demonstrate, and deploy fusion relevant multiphysics capabilities including electromagnetics, particle-in-cell plasma, tritium transport, and fusion blanket design. This new model is an expansion of the MOOSE-based plasma application, Zapdos, which was originally formulated to model low-temperature, non-magnetized plasma processes. Verification, benchmarking, and validation studies have been conducted. Verification studies involved utilizing the method of manufactured solutions and comparing the convergence slope of a known solution to the theoretical slope. Benchmarking consists of comparisons to existing edge codes, namely BOUT++ and SOLEDGE3X. Validation efforts focused on comparisons against open-source data from the TCV tokamak.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY

A Python Tool for Aqueous Plutonium Nitrate Density Law Input Preprocessing in MCNP6

Here, this work develops a predictive density tool in Python, named Plutonium Nitrate Solutions (PuNS), to reduce bias and uncertainty in nuclear criticality safety calculations for plutonium nitrate systems. The Pitzer method and an empirical method were implemented into the PuNS tool to generate atom densities for use in MCNP6 material cards. These material cards are directly prepared into an MCNP6 input text file and are calculated based on customizable user inputs of plutonium content, nitric acid content, temperature, and plutonium isotope weight percentages. The PuNS tool is validated and verified against the International Criticality Safety Benchmark Evaluation Project Handbook experiments and is observed to predict densities within a root mean square error of 0.89% for the Pitzer method and 1.82% for the empirical method. These errors in density lead to up to 1569 pcm difference in MCNP6 calculated k eff for the Pitzer method and up to a 1751 pcm difference for the empirical method when compared to experimental benchmarks. Simultaneous work is also being performed at Los Alamos National Laboratory and the University of New Mexico to create a similar tool for plutonium chloride solutions, named Plutonium Chloride Solution, which aims to provide the accreditation of the chlorine absorption. These capabilities will not only provide more accurate models but also facilitate an improved understanding of solution systems and a potential relaxation in the conservatism of current aqueous plutonium processing criticality safety limits.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Vidyut3d: A Gpu Accelerated Fluid Solver for Non-Equilibrium Plasmas on Adaptive Grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure twin electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate approximately 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

Sitaraman, Hariswaran

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units

Verification and Demonstration of One-Dimensional Freezing Model in SAM for Salt-Cooled Reactor Analysis Applications

This work presented the development and implementation of the one-dimensional freezing model in system analysis code, SAM, as well as code verification, and code demonstration during a postulated overcooling transient, for fluoride salt-cooled high-temperature reactor (FHR) system and safety analysis applications. The paper at first summarized the freezing model, finite element numerical method, and special numerical treatment for handling phase appearance/disappearance. Analytical solutions were derived for two cases (with and without solid walls) for code verifications purpose. As expected, numerical results predicted by the SAM code agreed very well with the analytical solution. A code demonstration was then performed on a postulated protected overcooling event transient of a generic reference PB-FHR design. The code was found to successfully predict salt freezing during such a postulated event. However, due to lack of salt freezing testing data, code validation has not been performed in this work, which will be pursued in later studies when such data becomes available.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Verification of the ENDF/B-VII.1 Based MC 2 -3 Library Rev.1

The MC 2 -3 code, developed by Argonne National Laboratory under the DOE-NE NEAMS program, is a multigroup cross section generation code for fast reactor applications. Last year, the ENDF/B-VII.0 (E70) MC 2 -3 library, which has been extensively used, verified, and validated over a long period, was intensively reverified and updated to support the commercial grade dedication (CGD) requirement of the TerraPower Natrium project. This year, the ENDF/B-VII.1 (E71) MC 2 -3 library, the preliminary version of which was generated several years ago, was regenerated and rigorously verified to support the Natrium project as well as the completion of verification of the E71 library. The E71 library was verified using the process developed during the verification of the E70 library, including comparisons of cross sections with the NJOY-generated cross sections, comparisons of the resolved resonance cross sections with those using the PEDNF library, and comparison of total cross sections with the sum of partial cross sections. Additional verifications were conducted to ensure that the benchmark problem solutions with the E71 library are reasonable compared to the corresponding Monte Carlo solutions. Furthermore, the E71 gamma library was generated, which includes data for prompt gamma, delayed gamma, and delayed beta as well as neutron and gamma heating. The gamma library was verified at the level of individual isotopes. The EBR-II core solutions from MC 2 -3/ DIF3D and MCNP were compared, demonstrating that those solutions in terms of k-effective and assembly powers were in good agreement.

22 GENERAL STUDIES OF NUCLEAR REACTORS

(Doublon) Benchmarking of Different Inverse Point Kinetics Implementations for an Autocorrected Reactimeter Algorithm

In November 2017, the Transient Reactor Test Facility returned to operation. Since that time, many transient test series have been completed, such as the Transient Heatsink Overpower Response capsule (THOR), the Transient Water Irradiation System for TREAT (TWIST), and Sirius. Each has provided valuable data for materials performance and reactor safety that can be applied in future designs. During each experimental series, detector count rates provided important information on the core behavior during transients. However, a limitation of these data is that variations in the neutron distribution during experiments can cause errors when attempting to infer reactivity evolution from detector signals. Neutron physics codes can be used to compute the flux shape variations. However, this is a poor solution when the experimental data is used for code verification, validation and uncertainty quantification. Indeed, if the output of the code is used both as a reference and to correct what the reference is compared to, the circular dependency limits the quality of the verification, validation and uncertainty quantification approach. To overcome this problem, the autocorrected reactimeter algorithm (ACRA) has been developed. This approach infers a time-dependent reactivity evolution by testing different spatial corrections and selecting the one that minimizes reactivity variations when the core is in a frozen configuration (i.e., when there is no variation in parameters affecting reactivity). However, the scope of this method was limited to transients where there were negligible thermal feedback. Indeed, the core is never in a frozen configuration when the fuel temperature varies during the whole transient. This is our motivation for developing an improved version of the ACRA that does not require frozen configurations. To develop this new algorithm, we need a precise and unbiased implementation of the inverse point kinetic equations (IPKEs) as any error in the reactivity evaluation will be propagated into the choice of the optimal spatial correction. Indeed, the previous reactimeter algorithm would use approximations, such as a negligible flux amplitude derivative, to focus on rapidity. For the numerical validation of ACRA, we aim at absolute error under for reactivity derived from signals similar to the one of this study. In this summary, we test eight different IPKE implementations. Each will process a mockup signal built for this study, similar to those that the future ACRA will process. Each reactivity output will be compared to the reference reactivity that has been used to generate the mockup signal. The implementation minimizing the difference with the reference reactivity will be used in the development of a new ACRA formulation.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS

Modeling of Macroscopic Dynamics in Three-Dimensional Plasma Configurations (Final Technical Report)

A numerical simulation-based study to investigate the stability properties of inherently three-dimensional plasma magnetic configurations is presented. These configurations, called stellarators and heliotrons, use external helical coils to provide the twisting magnetic field that is required to confine ionized plasma particles. In contrast to the tokamak configuration, which nominally has the property of axisymmetry, electrical current does not need to be induced in stellarator and heliotron plasma. Experiments have shown that these three-dimensional configurations are remarkably robust to macroscopic instability, even when driven to relatively high levels of plasma pressure. Our understanding of how the plasma is able to withstand macroscopic instability will be enhanced by the work proposed here. The effort will generalize existing numerical modeling capability, and it will apply the new capability to model macroscopic dynamics in these three-dimensional configurations. The development work has been applied to the NIMROD simulation code (https://nimrodteam.org) that was originally based on axisymmetric problem domains. It has been generalized to accommodate the three-dimensional shaping of the plasma volume in stellarators and heliotrons. Its use of equilibrium data has also been generalized, and the implementation allows different numerical representation of the magnetic field. Analysis has been performed to inform the selection of numerical methods, and a method to accelerate the iterative solution of the necessary algebraic systems has been developed and implemented. Verification of the new NIMSTELL code on benchmark problems has also been an important part of the effort.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

HARD: A performance portable radiation hydrodynamics code based on FleCSI framework

Hydrodynamics And Radiation Diffusion (HARD) is an open-source application for high-performance simulations of compressible hydrodynamics with radiation-diffusion coupling. Built on the FleCSI (Bergen et al., 2021 [1]) (Flexible Computational Science Infrastructure) framework, HARD expresses its computational units as tasks whose execution can be orchestrated by multiple back-end runtimes, including Legion (Bauer et al., 2012 [2]), MPI (Forum, 1994 [3]), and HPX (Kaiser et al., 2020 [4]). Node-level parallelism is handled through Kokkos (Edwards et al., 2014 [5]), providing a single-source, portable code base that runs efficiently on laptops, small homogeneous clusters, and the largest heterogeneous supercomputers currently available. To ensure scientific reliability, HARD includes a regression test suite that automatically reproduces canonical verification problems such as the Sod and LeBlanc shock tubes, and the Sedov blast wave, comparing numerical solutions against known analytical results. The project is distributed under an OSI-approved license, hosted on GitHub, and accompanied by reproducible build scripts and continuous integration workflows. This combination of performance portability, verification infrastructure, and community-focused development makes HARD a sustainable platform for advancing radiation hydrodynamics research across multiple domains.

97 MATHEMATICS AND COMPUTING

Verification of the PERSENT Software

Ongoing commercial design activities require a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system and substantial work has been done to verify its accuracy on several identified commercial needs. This manuscript details the verification work done on PERSENT which relies upon the DIF3D code for its forward and adjoint flux solution. Previous work identified the PERSENT features required to be verified to support commercial design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying PERSENT’s ability to correctly calculate four key quantities: perturbation worth distributions, kinetics parameters, sensitivity coefficients, and cross section uncertainty quantification. This manuscript provides the verification tasks and their results with respect to these quantities needed for commercial design activities. For the perturbation worth distributions, hand calculations are deployed to verify the PERSENT calculated results. Similarly, hand calculation of the PERSENT computed kinetics parameters is also used to verify the PERSENT results. In both of these, the input to PERSENT is manipulated to ensure the hand calculation exactly matches the equations PERSENT is calculating. The sensitivity coefficients involve calculating the derivatives of a parameter (such as reactivity worth), with respect to the cross section data. Direct finite difference calculations with DIF3D are used to verify the PERSENT calculated results. For the uncertainty quantification, manufactured input to PERSENT is used to allow an exact hand calculation to reproduce the PERSENT calculated results. The work detailed in this report verified that significant issues were identified for earlier versions of PERSENT for sensitivity coefficients which were corrected in this work and thus version 12.1.0 of PERSENT must be used to reproduce all of the verified work in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS

MOOSE-based Tritium Migration Analysis Program, Version 8 (TMAP8) for advanced open-source tritium transport and fuel cycle modeling

Tritium management is critical for the safety, sustainability, and economics of fusion energy systems, and advanced and reliable modeling tools help accelerate the development of tritium technologies. This paper presents the Tritium Migration Analysis Program, Version 8 (TMAP8), an open-source, MOOSE-based application developed to provide state-of-the-art tritium transport and fuel cycle modeling capabilities. TMAP8 aims to expand the capabilities of previous versions (i.e., TMAP4 and TMAP7) by leveraging modern computational techniques, ensuring high software quality assurance standards (key to building trust), and enabling multispecies, multiscale, and multiphysics simulations for integrated tritium transport modeling in complex geometries. This paper outlines TMAP8’s scope and rigorous development practices, emphasizing its transparency, accessibility, modularity, and reliability. We present the current suite of verification and validation cases based on those from TMAP4, demonstrating TMAP8’s accuracy and reliability against analytical solutions and experimental data. Additionally, the paper showcases TMAP8’s integrated fuel cycle modeling capabilities, highlighting its applicability at various scales and levels. The TMAP8 code and documentation are openly available, promoting collaborative development and widespread adoption within the fusion community. Future work will soon expand TMAP8’s verification and validation suite to include those from TMAP7 and other recent experimental studies for validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING