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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quasi-Dynamic Electromagnetic Field Safety Analysis and Mitigation for High-Power Dynamic Wireless Charging of Electric Vehicles

Dynamic wireless charging of electric vehicles (EV) is an emerging charging technology to enable non-contact wireless charging while the vehicle is moving. Compared to stationary wireless charging, in-motion wireless charging involves dynamic processes in which an EV is passing over the charging pads (transmitters). This in motion process makes the dynamic electromagnetic (EM) environment more complicated, and EM safety needs to be ensured under all circumstances. This is due to the fact that the entire vehicle body may be exposed to magnetic fields while the vehicle moves over the energized transmitter. This paper investigates several typical charging scenarios when EVs approach, pass over, and move away from the charging pads. Quasi-dynamic models, which are preliminarily verified by coils’ inductance measurements, are developed to analyze the dynamic process. Based on the quasi-dynamic analysis, shielding solutions are also studied to ensure EM safety for the dynamic wireless charging processes.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

MPACT Theory Manual, Version 2.2.0

This theory manual describes the three-dimensional (3-D) whole-core, pin-resolved transport calculation methodology employed in the MPACT code. To provide sub-pin level power distributions with sufficient accuracy, MPACT employs the method of characteristics (MOC) solutions in the framework of a 3-D coarse mesh finite difference (CMFD) formulation. MPACT provides a 3D MOC solution, but also a 2D/1D solution in which the 2D planar solution is provided by MOC and the axial coupling is resolved by one-dimensional (1-D) lower order (diffusion or P3) solutions. In Chapter 2 of the manual, the MOC methodology is described for calculating the regional angular and scalar fluxes from the Boltzmann transport equation. In Chapter 3, the 2D/1D methodology is described, together with the description of the CMFD iteration process involving dynamic homogenization and solution of the multigroup CMFD linear system. A description of the MPACT depletion algorithm is given in Chapter 4, followed by a discussion of the subgroup and ESSM resonance processing methods in Chapter 5. The final Chapter 6 describes a simplified thermal hydraulics model in MPACT.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

A Self-Limiting Electro-Ablation Technique for the Top-Down Synthesis of Large-Area Monolayer Flakes of 2D Materials

We report the discovery of an electrochemical process that converts two dimensional layered materials of arbitrary thicknesses into monolayers. The lateral dimensions of the monolayers obtained by the process within a few seconds time at room temperature were as large as 0.5 mm. The temporal and spatial dynamics of this physical phenomenon, studied on MoS2 flakes using ex-situ AFM imaging, Raman mapping, and photoluminescence measurements trace the origin of monolayer formation to a substrate-assisted self-limiting electrochemical ablation process. Electronic structure and atomistic calculations point to the interplay between three essential factors in the process: (1) strong covalent interaction of monolayer MoS2 with the substrate; (2) electric-field induced differences in Gibbs free energy of exfoliation; (3) dispersion of MoS2 in aqueous solution of hydrogen peroxide. This process was successful in obtaining monolayers of other 2D transition metal dichalcogenides, like WS2 and MoTe2 as well.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Two Modes of the Self-Similar Evolution of Charged Plasma

Two self-similar modes of evolution of charged particles’ high-current beam are described analytically. The situation being considered falls within the field of nonneutral plasma electrodynamics. The process is considered in terms of the nonlinear 1D evolution of the charge density w(x, t) in the channel of a longdistance transmission line with nonlinearly distributed resistance R, capacitance C, and inductance L: R = R(w), C = C(w), and L = 0. It is shown that initially the front of w(x, t) accelerates and then slows down. The description of the process in the channel is based on the charge conservation law. An idealized “kinematic” approach is used according to which an equation in two unknowns (charge density and current density in the channel) can be reduced to an equation in one unknown w(x, t). A strongly nonlinear wave process is studied. A discontinuous solution w(x, t) is constructed with a zero boundary condition at infinity. Such a model description can apply only for revealing the main qualitative features of a complex process. Analytical expressions for the variation in the evolution of the front velocity and perturbed area length are derived. An interrelation between the nonlinearity parameter of the process and the amount of charge in the interelectrode gap is suggested based on the experimental data for the evolution of streamers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effect of Adsorbed Carboxylates on the Dissolution of Boehmite Nanoplates in Highly Alkaline Solutions

Understanding the dissolution of boehmite in highly alkaline solutions is important to the processing of the complex nuclear wastes stored at the Hanford (WA) and Savannah River (SC) sites. Here, we report the adsorption of model carboxylate anions on boehmite nanoplates in alkaline solutions and their effects on subsequent boehmite dissolution in 3 M NaOH at 80 °C. Although expectedly lower than at circumneutral pH, adsorption of oxalate at pH 13 at room temperature was significant and remained so through a linear decrease to 3 M NaOH conditions with no evidence for the appearance of new phases. Modeling of the adsorption data and rate were consistent with the formation of outer-sphere surface complexes. By using these conditions to preload the boehmite nanoplates with oxalate, and separately acetate, we measured and compared their dissolution behavior at 80 °C and observed a clear suppression of the dissolution rate for the case of adsorbed oxalate by 23% and for adsorbed acetate by 10% compared to pure solids. Ex situ scanning electron microscopy (SEM) and transmission electron microscopy (TEM) characterization revealed no detectable difference in the morphologic evolution of the dissolving boehmite materials. In conclusion, we nonetheless conclude that pre-adsorbed carboxylate anions, even as nominally weakly bound outer-sphere complexes, can persist on the surface through highly alkaline conditions, decreasing the density of dissolution-active sites and thereby adding an extrinsic control on the dissolution rate.

Adsorption kinetics↗
DOE OSTI2023

Data-Driven Approaches for Bead Geometry Prediction Via Melt Pool Monitoring

In the realm of additive manufacturing, the selection of process parameters to avoid over and under deposition entails a time-consuming and resource-intensive trial-and-error approach. Given the distinct characteristics of each part geometry, there is a pressing need for advancing real-time process monitoring and control to ensure consistent and reliable part dimensional accuracy. Here, this research shows that support vector regression (SVR) and convolutional neural network (CNN) models offer a promising solution for real-time process control due to the models’ abilities to recognize complex, non-linear patterns with high accuracy. A novel experiment was designed to compare the performance of SVR and CNN models to indirectly detect bead height from a coaxial image of a melt pool from a single-layer, single bead build. The study showed that both SVR and CNN models trained on melt pool data collected from a coaxial optical camera can accurately predict the bead height with a mean absolute percentage error of 3.67% and 3.68%, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fluoride Analysis by Ion Chromatography in Support of Fast Critical Assembly (FCA) Spent Nuclear Fuel Processing

INTRODUCTION The Savannah River Site (SRS) is currently processing Fast Critical Assembly (FCA) fuel received from the Japan Atomic Energy Agency (JAEA) for disposition. Stainless steel-clad plate and rods in stainless steel containers are dissolved using electrolysis with a solution mixture of nitric acid (HNO3), potassium fluoride (KF), and gadolinium (Gd). An ion chromatography (IC) was developed and vetted to monitor fluoride at various sampling points of the process. To finalize the method, FCA test solution was analyzed to qualify the analytical method followed by real FCA process solution analysis using two different analytical columns. This presentation summarizes the development and vetting of the IC method.

White, Thomas L. [Savannah River National Laborato↗
DOE OSTI2023

Molecular Insight into the Effects of Clustering on the Dynamics of Ionomers in Solutions

Ionizable groups tethered to polymers enable their many current and potential applications. However, these functionalities drive the formation of physical networks through clustering of the ionic groups, resulting in constrained dynamics of the macromolecules. Understanding the molecular origin of this hindrance remains a critical fundamental question, whose solution will directly impact the processing of ionizable polymers from molecules to viable materials. Here, in this work, using quasielastic neutron scattering accompanied by molecular dynamics simulations, segmental dynamics of slightly sulfonated polystyrene is studied in solutions as the cohesion of the ionic assemblies is tuned. We find that in cyclohexane the ionic assemblies act as centers of confinement, affecting dynamics both on macroscopic lengths and in the vicinity of the ionic assemblies. Addition of a small amount of ethanol affects the packing of the ionizable groups within the assemblies, which in turn enhances the chain dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Production processing and workflow management software evaluation in the DUNE collaboration

The Deep Underground Neutrino Experiment (DUNE) will be theworld’s foremost neutrino detector when it begins taking data in the mid-2020s.Two prototype detectors, collectively known as ProtoDUNE, have begun tak-ing data at CERN and have accumulated over 3 PB of raw and reconstructeddata since September 2018. Particle interaction within liquid argon time projec-tion chambers are challenging to reconstruct, and the collaboration has set upa dedicated Production Processing group to perform centralized reconstructionof the large ProtoDUNE datasets as well as to generate large-scale Monte Carlosimulation. Part of the production infrastructure includes workflow manage-ment software and monitoring tools that are necessary to eciently submit andmonitor the large and diverse set of jobs needed to meet the experiment’s goals.We will give a brief overview of DUNE and ProtoDUNE, describe the varioustypes of jobs within the Production Processing group’s purview, and discuss thesoftware and workflow management strategies are currently in place to meetexisting demand. We will conclude with a description of our requirements in aworkflow management software solution and our planned evaluation process.

Herner, Kenneth R.↗
DOE OSTI2023

Demonstration of Scaled-Production of Rare Earth Oxides and Critical Materials from U. S. Coal-Based Sources (Final Report)

The project objective was to demonstrate scaled production of high purity rare earth oxides (REO), nominally exceeding 90% grade, from coal refuse sources using innovative technologies that reduce cost and improve environmental outcomes relative to traditional rare earth processing technologies. The project utilized a critical material pilot plant constructed and tested as part of a previous U.S. Department of Energy project. Target performance criteria was a 50% reduction in production cost based on previous optimum values, 150% increase in recovery and greater than 2% concentrates of rare earth oxides, cobalt and manganese. Concentrate production goals were to produce a rare earth mix oxide product at a rate of 200 grams per day having a minimum purity of 50% as well as products of cobalt and manganese having a minimum purity of 2%. A previous pilot plant investigation identified acid cost as the major contributor to an operating cost that made the recovery of rare earth and other critical metals from bituminous coal sources economically challenging. As such, acid cost reduction was a major target using bio-oxidation reactors to produce sulfuric acid from naturally occurring coal pyrite. Based on laboratory data, a bio-oxidation circuit was designed for the pilot plant to produce 7.5 l/min of acid using two 11-m3 (3000 gallon) reactors equipped with 40 hp aerators for air dispersion. The pilot-scale tests revealed that acid concentration equivalent to as high as 1.0 M sulfuric acid could be continuously produced. However, the bio-acid contained exceptionally high iron concentrations, which complicated downstream processing of the pregnant leach solution (PLS). A TEA of the bio-oxidation circuit showed that production cost was approximately $0.13 per kg acid equivalent if produced using a four-day retention time in the reactors. This value represents a 48% reduction from that of purchased bulk sulfuric acid. Calcination (or roasting) studies were conducted on coarse refuse from West Kentucky No. 13 and Fire Clay coal seam sources. The test results revealed the potential to increase recovery by nearly 100% using temperatures between 500°C to 700°C with light REE recovery value being the most improved. Acid baking of the calcined products using sulfuric acid at 250°C increased heavy rare earth recovery from around 40% to 80% while decreasing the acid requirements by over 50%. The existing pilot plant was upgraded for the pilot scale demonstration of REE and CM recovery. The primary feedstocks were West Kentucky No.13 and heap leach pregnant leach solution (PLS) while a secondary feedstock was a lignite waste material from a construction sand operation. The pilot scale operation started with PLS generation through leaching followed by iron and aluminum removal, nominally at 3.3 and 4.5 pH, respectively. Leaching lixiviants used for the test were industrial grade sulfuric acid or bio-acid generated at the pilot scale facility. For most of the tests, the solid feed rate was 200 lb/hr whereas lixiviant was added at 2 gpm to provide an optimal residence time of 45 minutes. Following the contaminant removal step, several different process schematics were tested with the goal of maximizing REE recovery and purity. In the first test, direct processing of aluminum precipitation raffinate for REE recovery using oxalic acid at pH 1.5 was investigated. Overall REE recovery was approximately 45%. Unfortunately, elevated calcium content in the PLS significantly impacted the RE-Oxide product grade. Similarly, high calcium content decreased both the product purity and grades of CM products. As such, a new flowsheet was tested with the same initial process schematic but different precipitation stages for REEs and CMs at pH 6.0 and 9.0, respectively. It was noted that the overlapping precipitation behavior of Co, Ni and Zn with REEs limited the applicability of this process schematic. While this change increased the RE-Oxide grade from 36% in the first test to 87%, the loss of critical metals to the REE cake and bypass of the REEs to the CM cake significantly impacted the recovery of both REEs and CMs. Therefore, the modified process flowsheet combined oxalic acid precipitation stage raffinate and redissolved CM cake filtrate to maximize both the recovery and purity of the products. Consequently, a RE-Oxide product with 85% purity and CM cakes with over 19% Co, 38% Ni, 14% Zn and 9% Mn content were generated with significantly higher recoveries. While the modified process flowsheet improved recoveries and grades, elemental losses observed in separate precipitation and redissolution losses inspired the adaptation of a single precipitation stage at pH 9.0 for both REEs and CMs. This change was anticipated to maximize the REE recovery while minimizing the costs associated with separated redissolution and processing stages. As expected, REE recovery in this new circuit arrangement was over 56% with a product grade of over 87% RE-Oxide content. Similarly, Co, Ni, Mn, and Zn recoveries of 54%, 40%, 67%, and 66%, respectively, were achieved. Unfortunately, the elevated calcium content present in the solution due to its precipitation at pH 9.0 caused a decrease in the CM cake quality. Therefore, the final process flowsheet involved the addition of calcium oxalate precipitation following the oxalic acid precipitation stage, which effectively eliminated calcium contamination of the CM products. Finally, the pilot scale experiments conducted using bio-acid achieved comparable REE leaching recoveries to the conventional sulfuric acid leaching. Elevated iron concentration in the solution caused the co-precipitation of REEs with the iron and aluminum cake, resulting in the REE losses. Furthermore, elevated iron content bypassing the iron and aluminum precipitation stages contaminated the metal sulfide and manganese cake, respectively. A techno-economic analysis was performed based on a commercial facility capable of treating 500 tph of coal-based material. The production cost for West Kentucky No. 13 coarse refuse material ranged from approximately $500-$700/kg of total rare earth oxide whereas the lignite source had significantly lower production cost of $100-$300/kg. The significant difference in cost was due to the easier leaching characteristics of the lignite material and the higher feed concentrations. All process scenarios resulted in a negative net present value (NPV). For the lignite feedstock, laboratory REE leach recovery values were about 30% higher than the pilot plant data. Using the lab leach results, a positive net present value was achieved and the production cost decreased from $100-$300 $/kg to less than $150/kg of total REO.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2022

Scalable branching on dual decomposition of stochastic mixed-integer programming problems

In this work, we present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caroe and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including (1) branching on the optimal solutions of the Dantzig-Wolfe reformulation of the restricted master problem and (2) using a more comprehensive (yet simple) measure for the dispersions associated with subproblem solution infeasibility. We prove that the proposed branching process leads to an algorithm that terminates finitely, and we provide conditions under which globally optimal solutions can be identified after termination. We have implemented our new branching method, as well as the Caroe-Schultz method and a branch-and-price method, in the open-source software package DSP. Using SIPLIB test instances, we present extensive numerical results to demonstrate that the proposed branching method significantly reduces the number of node subproblems and solution times.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Integrated titanium dioxide (TiO{sub 2}) nanoparticles on interdigitated device electrodes (IDEs) for pH analysis

Titanium dioxide (TiO{sub 2}) nanoparticles based Interdigitated Device Electrodes (IDEs) Nanobiosensor device was developed for intracellular biochemical detection. Fabrication and characterization of pH sensors using IDE nanocoated with TiO{sub 2} was studied in this paper. In this paper, a preliminary assessment of this intracellular sensor with electrical measurement under different pH levels. 3-aminopropyltriethoxysilane (APTES) was used to enhance the sensitivity of titanium dioxide layer as well as able to provide surface modification by undergoing protonation and deprotonation process. Different types of pH solution provide different resistivity and conductivity towards the surface. Base solution has the higher current compared to an acid solution. Amine and oxide functionalized TiO{sub 2} based IDE exhibit pH-dependent could be understood in terms of the change in surface charge during protonation and deprotonation. The simple fabrication process, high sensitivity, and fast response of the TiO{sub 2} based IDEs facilitate their applications in a wide range of areas. The small size of semiconductor TiO{sub 2} based IDE for sensitive, label-free, real time detection of a wide range of biological species could be explored in vivo diagnostics and array-based screening.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

IDAES-PSE 2.6.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. IDAES-PSE 2.6.0 Release Highlights Upcoming Changes IDAES will be switching to the new Pyomo solver interface in the next release. Whilst this will hopefully be a smooth transition for most users, there are a few important changes to be aware of. The new solver interface uses a different version of the IPOPT writer (“ipopt_v2”) and thus any custom configuration options you might have set for IPOPT will not carry over and will need to be reset. By default, the new Pyomo linear presolver will be activated with ipopt_v2. Whilst are working to identify any bugs in the presolver, it is possible that some edge cases will remain. IDAES will begin deploying a new set of scaling tools and APIs over the next few releases that make use of the new solver writers. The old scaling tools and APIs will remain for backward compatibility but will begin to be deprecated. New Models, Tools and Features New Intersphinx extension automatically linking Jupyter notebook examples to project documentation New end-to-end diagnostics example demonstrated on a real problem New complementarity formulation for VLE with cubic equations of state, backward compatibility for old formulation New solver interface with presolve (ipopt_v2) in support of upcoming changes to the initialization and APIs methods, with default set to ipopt to maintain backwards compatibility; this will deprecate once all examples have been updated New forecaster and parameterized bidder methods within grid integration library Updated surrogates API and examples to support Keras 3, with backwards compatibility for older formats such as TensorFlow SavedModel (TFSM) Updated costing base dictionary to include the 2023 cost year index value Updated ProcessBlock to include information on the constructing block class Updated Flowsheet Visualizer to allow visualize() method to return value and functions Bug Fixes Fixed bug in the Modular Property Framework that would cause errors when trying to use phase-based material balances with phase equilibria. Fixed bug in Modular Properties Framework that caused errors when initializing models with non-vapor-liquid phase equilibria. Fixed typos flagged by June update to crate-ci/typos and removed DMF-related exceptions Minor corrections of units of measurement handling in power plant waste/transport costing expressions, control volume material holdup expressions, and BTX property package parameters Fixed throwing >7500 numpy deprecation warnings by replacing scalar value assignment with element extraction and item iteration calls Testing and Robustness Migrated slow tests (>10s) to integration, impacting test coverage but also yielding a nearly 30% decrease in local test runtime Pinned pint to avoid issues with older supported Python versions Pinned codecov versions to avoid tokenless upload behavior with latest version Bumped extensions to version 3.4.2 to allow pointing to non-standard install location Deprecations and Removals Python 3.8 is no longer supported. The supported Python versions are 3.9 through 3.12 The Data Management Framework (DMF) is no longer supported. Importing idaes.core.dmf will cause a deprecation warning to be displayed until the next release The SOFC Keras surrogates have been removed. The current version of the SOFC surrogate model in the examples repository is a PySMO Kriging model.

AS↗
DOE OSTI2025

IDAES-PSE 2.8.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications.

AS↗
DOE OSTI2019

Implementation and Verification of Isolated Defects for GTS Lifecycle Analyses

Often, the presence of cracks in manufactured components are detrimental to their overall performance. We develop a workflow and tools in this report using CUBIT and Sierra/SM for generating and modeling crack defects to better understand their impact on such components. To this end, we provide a CUBIT library of various prototypical crack defects embedded in pipes and plates that can be readily used in a wide range of simulations, with specific application to those used in Gas Transfer Systems (GTS). We verify the accuracy of the J-integral post-processing capability in Sierra against solutions available in existing literature for the cracks and geometries of interest within the context of linear elastic fracture mechanics, and describe ongoing efforts to quantify and assess numerical errors. Through this process, we outline overall suggestions and recommendations to the user based on the proposed workflow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis

Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process—called code verification—ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second-order accurate finite elements and a variety of time-integration schemes. Furthermore, these results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗