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At least 289 records · Page 16

Technoeconomic Analysis of the Electrochemically Mediated Amine Regeneration CO 2 Capture Process

The electrochemically mediated amine regeneration (EMAR) process presents an alternative route to the conventional thermal amine regeneration for carbon capture from a flue gas source. In this study, we conducted an economic analysis on the EMAR system for postcombustion CO2 capture from a 550 MWe power plant capturing 3.1 MtCO2 annually and from a mini steel mill with annual capture close to 170 ktCO2. We followed the recommendation of the National Energy Technology Laboratory (NETL) 2010 report to estimate the cost of CO2 avoided ([$/tCO2]). Detailed cost modeling of the electrochemical separation stage was conducted. This is integrated with the entire process flowsheet (e.g., including absorber, compressor, pumps, and other auxiliary equipment). Here, we identified the membrane cost as the dominant capital cost for the electrochemical separation train. At a membrane unit price of less than 10/m2, the CO2 capture cost can be reduced to below 50/tCO2 with optimized process conditions (e.g., desorption pressure and utilization of waste heat). Improvements in process design, cell construction, and solvent formulation may lead to additional reductions in the CO2 capture cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fabricating Single Crystal Quantum Dot Solids

The central goal of this research program was to establish fundamental synthesis and processing principles to enable the fabrication of single crystal quantum dot solids (QDS) with programmable structure (i.e., hexagonal and square) and composition. Our approach towards that goal leveraged access to and experience with unique in-situ, multi-probe characterization techniques to understand and ultimately control the fundamental relationship between processing conditions and nucleation and growth of QDS. The program integrated synthesis and fabrication (Hanrath) with in-situ TEM analysis (Kourkoutis) and computational modeling (Clancy) to gain atomic-level insights into the underlying physical phenomena governing assembly and attachment and to guide the development of optimized processing methods. We have established a foundational understanding of physicochemical interactions of self-assembly at a fluid interface, superlattice structure transformation pathways, the critical role of disorder during the initial dimerization of colloidal quantum dot monomers, and the residual strain distribution within the inter-dot epitaxial bridge which hampers the formation of novel electronics states of the quantum dot solids. Collectively, these insights have contributed towards advancing the mechanistic understanding of the complex choreography of assembly and attachment as well as understanding what currently limits further advances in high-fidelity quantum dot solids and tiles.

36 MATERIALS SCIENCE↗

The efficacy of Lewis affinity scale metrics to represent solvent interactions with reagent salts in all-inorganic metal halide perovskite solutions

Solvents employed in the solution processing of metal halide perovskites are known to play a key role in defining the morphology and properties of the resulting thin film, and thus the performance of perovskite solar cell devices. Accurate metrics are needed that are capable of differentiating among candidates, finding solvents that adequately solubilize the various precursor species in solution and facilitate the nucleation and growth of these materials. Existing metrics such as the unsaturated Mayer bond order (UMBO) and the Gutmann donor number (DN) have been tested for lead iodide perovskite systems; but there has yet to be a comprehensive study on their transferability to lead-free perovskite solutions. Here, we use ab initio methods (density functional theory) and regression analysis tools to study the usefulness of DN and BF 3 affinity scales in this regard. We compared the relative effectiveness of these scales to describe interactions between solvents and BXn perovskite salts of lead (Pb 2+ ), tin (Sn 2+ and Sn 4+ ), germanium (Ge 2+ ), bismuth (Bi 3+ ), and antimony (Sb 3+ and Sb 5+ ). The DN proved to be a better representation than the BF 3 of such interactions, reflecting the closer similarity of these species to the “parent” SbCl 5 Lewis acid than to BF 3 . In addition, we have uncovered the usefulness of the lithium cation affinity metric (LCA) to describe the strength of interactions between solvents and A-site cations (e.g. Na + , K + , Rb + and Cs + ) in all-inorganic metal halide perovskite solutions. We find that the coordination strengths of solvents towards species in all-inorganic metal halide perovskite solutions are best described by two different metrics with distinct modes of action: DN differentiates among BX n salt complexes, and LCA among A-site cation species. This revelation can help guide the choice of solvent to optimize processing conditions. It also emphasizes the importance of selecting solvents whose DN and LCA optimize coordination to key Lewis acid species in all-inorganic perovskite solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimization and Evaluation of Energy Savings for Connected and Autonomous Off-Road Vehicles

Off-road vehicles, such as wheel loaders, excavators, and harvesters, are extensively utilized across a wide range of industries, including construction, agriculture, and mining. These machines have become indispensable in supporting the day-to-day operational needs of a nation, playing a critical role in various sectors' infrastructure and productivity. However, despite their utility, off-road vehicles are significant consumers of fossil fuels, resulting in substantial emissions that contribute to environmental degradation. This highlights the pressing need for research and technological advancements aimed at improving their energy efficiency and reducing their carbon footprint. There are, however, two primary challenges that must be addressed to achieve these goals. First, off-road vehicles typically perform both driving and working tasks simultaneously, which introduces a high level of complexity into their overall dynamic systems. Analysis the interactions between these functions is challenging. Second, research into off-road vehicles is inherently interdisciplinary, demanding expertise across several domains such as fluid power systems, vehicle dynamics, control theory, optimization techniques, and real-world implementation. Recognizing these challenges, we proposed the project titled "Optimization and Evaluation of Energy Savings for Connected and Autonomous Off-Road Vehicles" as a comprehensive solution to enhance fuel efficiency while simultaneously improving productivity. This project specifically focuses on autonomous off-road vehicles, with particular attention to wheel loaders, and seeks to develop novel methods to optimize energy consumption without sacrificing operational performance. The project integrates real-time control algorithms, vehicle dynamics modeling, and co-optimization of powertrain system and vehicle system to achieve these goals. Our optimization strategy dynamically co-optimizes critical parameters at both the powertrain and vehicle levels, including vehicle speed, working tool movements, powertrain dynamics, and engine operations in real-time. To streamline this optimization process, we developed a vehicle model that captures the key dynamics while significantly enhancing computational efficiency. This allows the system to intelligently minimize fuel consumption, all while maintaining or even improving productivity through real-time calculations during various off-road operations. To validate the effectiveness of this energy optimization method, we introduced a state-of-the-art Hardware-in-the-Loop (HIL) testbed. This reconfigurable testbed seamlessly integrates the actual engine with virtual models of the wheel loader's subsystems, allowing for accurate emulation of real-world operational loads and environments. By simulating these conditions, the HIL testbed enables us to evaluate the wheel loader’s performance under diverse working scenarios, ensuring the developed solution is applicable in real-world operations. This testbed proved to be instrumental in validating the optimization algorithms and demonstrating the system's practical effectiveness. During the evaluation and testing phase, we employed the HIL testbed to rigorously assess the energy savings and productivity improvements generated by the optimized system. The results were highly encouraging, revealing that the automated wheel loader achieved over 30% fuel savings compared to traditional, human-operated cycles, with comparable or even enhanced levels of productivity. The insights gained from this HIL-based testing provided critical validation of our approach and highlighted the potential for deploying these optimized autonomous technologies in real-world off-road vehicles.

33 ADVANCED PROPULSION SYSTEMS↗

How to Minimize Faradaic Efficiency Error in Electrochemical CO 2 Reduction for Gas Products

Faradaic efficiency (FE) is an important metric for evaluating electrochemical processes, such as carbon dioxide reduction, that is often used for performance comparisons. Although the equation to calculate FE is well-known, details needed to yield accurate values are often overlooked, potentially leading to errors exceeding 100%. Avoiding any errors is crucial for drawing correct conclusions, especially during a catalysis optimization process. Factors with high potential for FE errors include incorrect mass flow rates and temperature values, imprecise gas chromatography calibrations, and uncorrected gas viscosities, while factors with less potential are also identified. In conclusion, this manuscript presents FE calculation guidelines intended for both newcomers and experts in the field of electrochemical fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

System and method to facilitate a search for a hybrid-manufacturing process plan

One embodiment of the present disclosure provides a system and method for facilitating a search for a hybrid-manufacturing process plan for manufacturing an object. During operation, the system can obtain a set of partial order constraints constraining the order in which a set of at least two manufacturing actions, corresponding to addition or removal of predefined regions of space, appear in a process plan. The system can constrain, based on the set of partial order constraints, a search space. The search space can correspond to a tree in which the nodes represent the object's state and the edges represent available actions at each node. The system can then determine a set of optimized process plans represented by orderings of the actions, corresponding to paths on the search tree, that produce the desired final state in a cost-effective manner.

Crawford, Lara S.↗

Data-driven chemical kinetic reaction mechanism for F-24 jet fuel ignition

A data-driven chemical kinetic mechanism for the military version of Jet A, F-24, is developed for numerical simulations of the ignition process. The main purpose of this study is to obtain a practical F-24 mechanism across wide temperature and equivalence ratio ranges, with a particular focus on the negative temperature coefficient and low temperature regions. The new mechanism (ARLMech-HC-F24) is based on the HyChem model of a similar fuel and optimized using a micro-genetic algorithm against an experimental ignition delay data set of the target fuel. The development and optimization processes include reaction selection, population creation, shuffled tournament implementation based on a merit function, and child-individual creation for the next generation. Several techniques and parameters are proposed to generate an accurate mechanism through an efficient process. The newly introduced data-driven mechanism based on these techniques shows better merit value convergence and represents the ignition behavior more accurately than that without the techniques. This practical mechanism is suitable for the numerical simulations of the F-24 or Jet A ignition problem, and the suggested strategies can be employed in similar problems of rate coefficients estimation.

42 ENGINEERING↗

A Gaussian process autoregressive model capturing microstructure evolution paths in a Ni–Mo–Nb alloy

Additive manufacturing is increasingly being employed to produce components of complex geometries in structural alloys because of the expected energy savings associated with the near-net-shape capability and the ability to build in novel internal features that are not possible with many conventional manufacturing approaches. However, because of the extreme thermal conditions encountered, the non-equilibrium microstructures produced during powder bed-based additive manufacturing processes must be subjected to custom post-heat treatment processes to recover the target mechanical properties. Phase-field models and simulation techniques have matured to a state where the microstructure evolution paths, and the morphologies of the resulting precipitate phases can be predicted reasonably accurately, considering alloy-specific thermodynamic and kinetic aspects of the nucleation and growth processes. However, phase-field simulations are computationally intensive, which precludes the ability to apply the simulations directly to the length scale of the entire component. Therefore, it is highly desirable to develop low-computational-cost surrogate models that effectively capture the physics at the microstructural length scale, while facilitating the design of optimized processing conditions resulting in location-specific targeted microstructures at the component scale. The work presented here demonstrates the application of the materials knowledge system framework to develop a surrogate model that effectively captures the microstructural path during annealing of a Ni–Mo–Nb alloy containing different Mo and Nb compositions known to segregate during solidification under additive manufacturing conditions. Specifically, the surrogate model built in this work is based on a Gaussian process autoregressive model informed by statistical representation of simulated microstructures using two-point correlations and dimensionality reduction through principal component analysis. In conclusion, this surrogate model is shown to capture the bifurcation of the microstructural path during precipitation, which yields a microstructure dominated by the $\gamma^{\prime\prime}$ phase at high Nb concentrations and the $\delta$ phase at low Nb concentrations.

36 MATERIALS SCIENCE↗

Use Cases and Model Development of Thermal Storage Coupling for Advanced Nuclear Reactors

This report discusses the different options for coupling thermal energy storage (TES) systems to advanced nuclear power plants (A-NPPs) in order to enable flexible and hybrid plant operation. An advanced light-water reactor (ALWR) and a high-temperature gas-cooled reactor (HTGR) were selected as the initial use cases for demonstrating a thermally balanced energy storage coupling design for thermal power extraction. Cost functions for the A-LWR were derived from the fully balanced models that were developed based on three different coupling options with three different thermal energy bypass ratios. For the next steps, cost functions for the HTGR will also be derived, and additional nuclear reactors (e.g., a liquid-cooled fast reactor [LFR] or molten-salt reactor [MSR]) will be evaluated for coupling with TES in similar fashion, including the evaluation of their steady-state condition models and cost functions. The models presented herein showcase several design considerations, focusing on optimal deployment methodologies for achieving steady-state operation with minimum disruption to the nuclear power generation cycle. This report presents the results of steady state models developed using Aspen HYSYS®, wherein the thermal energy bypass for an NPP-TES coupling was varied up to 50%. The various components were sized using Aspen Process Economic Analyzer (APEA) and Aspen Exchanger Design and Rating (EDR), when applicable. Cost functions from these models were developed using the latest publicly available data obtained from APEA V11. The current steady-state models and cost functions provide a baseline for additional work focusing on dynamic operation and process optimization by using Idaho National Laboratory (INL)’s Framework for Optimization of Resources and Economics (FORCE) tools to evaluate the technoeconomic viability and transient operations of TES-coupled A-NPPs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Design of Novel Hot Gas Path Component for Gas Turbine Engines Enabled by Materials and Additive Manufacturing Process Development

This report covers the activities associated with the development and evaluation of two high-γ’ superalloys that were designed by external partners on this project, namely Carpenter Technologies Corporation and the University of California-Santa Barbra. One alloy was GammaPrint-700, a cobalt-base superalloy, and the other a nickel-base (Ni-base) superalloy GammaPrint-1100. Both were found to be printable through laser powder bed fusion (LPBF) additive manufacturing, with optimal process parameter sets being identified for each alloy. Further, high temperature mechanical testing was conducted on each alloy that showed both materials performed better than the comparative baseline (LPBF Hastelloy X), with the Ni-base superalloy being down-selected for scaling and printing of the tip shoe components.

36 MATERIALS SCIENCE↗

Probabilistic Hydropower Flexibility Valuation: Case Studies for Boating Flow Regime

The optimal scheduling of hydropower generation holds significant importance to power system operation. The unique requirements of environmental constraints and the power system, depending on their respective objectives, demand distinct flow patterns. While power system stakeholders strive to optimize revenue in electricity markets, stakeholders from boating recreation seeks to identify flow ranges that optimize the boating experience. In pursuit of a win-win solution, this study aims to reconcile the interests of various stakeholders in hydropower scheduling. The maximum revenue from day-ahead electricity market is explored through an optimization process considering both plant operation constraints, boating flow constraints, water availability, and market prices. Results of real world case studies at a river in California show that the proposed approach can achieve dual objectives: maximizing market revenue while addressing boating recreation necessities. In addition, as the accuracy of electricity price forecasting and flow forecasting increase, the optimal revenue becomes increasingly advantageous to hydropower plant operators.

13 HYDRO ENERGY↗

PHOENIX Electrostatic Design

PHOENIX (Portable, High-efficiency, Optimal ENergy Imaging X-rays) is a quasi-DC, electrostatic, vacuum-diode designed as a portable x-ray source with national defense and commercial applications. The patent-pending PHOENIX concept combines a megavoltage, Cockroft-Walton voltage multiplier with a Van de-Graaff electrostatic charge-storage dome to create a vacuum-diode suitable for x-ray production. Naturally this structure must minimize internal electric fields to reduce electrical breakdown while simultaneously reducing size and weight to enhance portability. In this paper we describe the optimization process and model results obtained using the COMSOL multi-physics code. We describe three models: a prototype model built to demonstrate the PHOENIX concept as part of Laboratory Directed Research and Development (LDRD) Mission Foundation Research (MFR) Phase-I , a “back-of-the-envelope” design used as a starting point for further COMSOL optimization, and finally, the optimized geometry implemented in the MFR Phase-II. In all cases compromises resulting from cost, schedule, and manufacturing constraints were taken into account as the design progressed.

42 ENGINEERING↗

PDPTW-DB: MILP-Based Offline Route Planning for PDPTW with Driver Breaks

The Pickup and Delivery Problem with Time Windows (PDPTW) involves optimizing routes for vehicles to meet pickup and delivery requests within specific time constraints, a challenge commonly faced in logistics and transportation. Microtransit, a flexible and demand-responsive service using smaller vehicles within defined zones, can be effectively modeled as a PDPTW. Yet, the need for driver breaks—a key human constraint—is frequently overlooked in PDPTW solutions, despite being necessary for regulatory compliance. This study presents a novel mixed-integer linear programming formulation for the Pickup and Delivery Problem with Time Windows and Driver Breaks (PDPTW-DB). To the best of our knowledge this formulation is the first to consider mandatory periodic driver breaks within optimized Microtransit routes. The proposed model incorporates regulatory compliant break scheduling directly within the vehicle routing optimization framework. By considering driver break requirements as an integral component of the optimization process, rather than as a post-processing step, the model enables the generation of routes that respect hours of service regulations while minimizing operational costs. This integrated approach facilitates the generation of schedules that are operationally efficient and prioritize driver welfare through driver breaks. We work with a public transit agency from the southern USA, and highlight the specific nuances of driver break optimization, and present a Pickup and Delivery Problem with Time Windows formulation for optimizing Microtransit operations and scheduling driver breaks. We validate our approach using real-world data from the transit agency. Our results validate our formulation in producing cost-effective, and regulation-compliant solutions.

Applied Computing, Transportation↗

Advanced Structured Adsorbent Architectures for Transformative Carbon Dioxide Capture Performance (Final Report)

Svante is a world leader at using solid sorbents for low-cost Carbon Dioxide (CO 2 ) capture, a technology which is recognized as critical in meeting the dual mandates of energy security/reliability and the mitigation of man-made CO 2 emissions. Svante has been developing proprietary adsorbent material compositions, forming them into structured laminates, developing and optimizing process cycles, and system design for efficient capture of CO 2 from post-combustion flue gases of thermal power plants and industrial facilities. The deployment of first-generation CO 2 capture technology has been significantly hampered by high costs and energy penalties, among other barriers. Second generation CO 2 capture technologies (including the Mark I variant of Svante’s Veloxotherm™ adsorption-based technology), utilizing single adsorbent architecture, show promise for reducing the barriers to deploying CO 2 capture plants in commercially meaningful numbers. The objective of this project was to evaluate the Recipient’s transformational (Mark-II) VeloxoTherm™ Technology via the development and bench-scale testing of an advanced structured adsorbent, including novel Bi-layer, laminated adsorbent structures and segmented beds. Svante selected, synthesized, and characterized tailored solid adsorbents for computational modeling, advanced structured adsorbent development, process simulations, and dynamic bench scale (~1-10 kg/day CO 2 captured) testing using an existing single-bed VeloxoTherm™ Station (VTS) coupled with a natural gas-fired boiler. Segmented beds used the in-house, multi-bed Process Demonstration Unit (PDU) to demonstrate key performance indicators (KPIs), such as recovery, product purity, regeneration energy, and the integrated system's productivity in lifetime analysis. Segmented beds were used at a 1 tonne per day (TPD) unit at an industrial site to provide bench-scale validation of performance in an industrial setting. Svante was developing and optimizing the post-combustion CO 2 adsorption technology architectures, including the Bi-layer and segmented laminated adsorbent structure design, integrated rapid cycle temperature swing adsorption (RC-TSA) cycle, flow path architecture, and adsorbent bed construction and packaging (including gas porting) to progress towards achievement of DOE’s Transformational CO 2 Capture goals of 95% CO 2 purity and a cost of electricity at least 30% lower than a supercritical Pulverized Coal (PC) power plant with CO 2 capture, or approximately $30 per tonne of CO 2 captured ready for demonstration by 2030. The main requirements to reach the DOE target cost of carbon capture below $30/MT using Rapid-Cycling Temperature Swing Adsorption (RC-TSA) are as follows: (1) Increased capacity at different CO 2 concentrations, (2) Increased sorbents cycle life, (3) Increased O 2 resistance, and (4) Decreased steam requirement to extract 1 kg of CO 2 .

20 FOSSIL-FUELED POWER PLANTS↗

Leverage modern artificial intelligence (AI) enabled systems for waste reduction

Manufacturing industries continue to face challenges in reducing waste, as upstream strategies such as source reduction and product redesign require a deeper understanding of processes compared to conventional recycling methods. Recent advancements in artificial intelligence (AI) and machine learning (ML) have opened new opportunities to integrate modern computational techniques with traditional waste minimization strategies. This paper explores AI-enabled approaches for product redesign, source reduction, and recycling that can significantly reduce waste generation while improving efficiency and sustainability. AI-driven material substitution and lightweighting in product design enable discovery of novel materials with optimized properties, reducing waste without compromising performance. Reinforcement learning models optimize process parameters, raw material specifications, and machine sequencing to minimize production losses, while Industrial Internet of Things (IIoT) systems paired with AI analytics enhance real-time waste tracking, predictive maintenance, and quality inspection. Furthermore, AI-based demand forecasting and production planning reduce overproduction and excess inventory, as demonstrated in industrial applications. In recycling, ML-powered pattern recognition and robotic sorting technologies achieve higher accuracy in waste segregation, directly improving recycling efficiency. Complementary solutions such as smart bins and AI-enabled waste pickup scheduling optimize collection logistics, reducing both costs and emissions. Although implementation requires upfront investment in infrastructure and training, the long-term benefits include higher material efficiency, reduced waste, improved product quality, and stronger sustainability outcomes across the supply chain. By leveraging AI-enabled systems, manufacturers can align waste minimization efforts with circular economy principles, creating scalable solutions for both industry and society.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Quantitative Understanding and Implementation of Screen Printed p+ Poly-Si/Oxide Passivated Contact to Enhance the Efficiency of p-PERC Cells

This paper reports on the modeling, optimization and implementation of p-TOPCon (tunnel oxide passivated contacts) on the rear side of a PERC to enhance its efficiency. Local Al-BSF of a traditional PERC was replaced by p+ polySi/oxide passivated contact composed of ~15Å thick chemically grown tunnel oxide, capped with 120-250nm thick p+ poly-Si layer grown by LPCVD. Process optimization resulted in full area unmetallized saturated current density (Jo) of ~ 5fA/cm2 for planar surface, nearly independent of poly-Si thickness in the range. Metallized J0 showed an increase with decreased poly-Si thickness and was found to be 9.6 and ~25fA/cm2 for 250nm and 120 nm polySi, respectively, with 4.6% direct metal-Si contact fraction, suitable for bifacial cells. A 21.4% efficient baseline PERC cell with local BSF was fabricated and analyzed to extract the rear side saturation current density (J0b’) of 66fA/cm2. Model calculations showed that by replacing this local BSF with 250nm TopCon developed in the study showed some Voc enhancement of 7mV, consistent with the observed Voc increase of 10mV. Model calculations also reveal that a more advanced LBSF PERC with better bulk lifetime and emitter saturation current density can extends its potential gain up to 0.4% in cell efficiency from the integration of p-TOPCon.

14 SOLAR ENERGY↗

Embedding Sensors in 3D Printed Metal Structures

The Transformational Challenge Reactor (TCR) program is leveraging recent advances in modeling and simulation, materials, and additive manufacturing (AM) technologies to design a modern nuclear reactor. Some of the main TCR technologies include in situ monitoring and the integration of sensors during the manufacturing of quality-significant nuclear reactor components. This report describes the general procedure and process optimization for embedding sensors within generic stainless steel 316 (SS316) components using laser powder bed fusion (LPBF). A more detailed, quality-significant test plan and supporting procedures are available upon request (ORNL/TM-2021/2127). LPBF involves the use of a scanning laser to selectively melt regions of a powder bed, additively building a part layer by layer. This report describes the LPBF processing technique and discusses the effects of LPBF processing parameters on the success of the sensor embedding process. Experiments used machined cavities in the form of channels in an SS316 base for the sensors to lay in while material is additively built over the top, thereby embedding them in an SS316 matrix. A preliminary investigation involved using empty SS316 sheaths as surrogates to explore the effects of various LPBF processing parameters and the dimensional requirements of the machined channels. Microstructural investigations showed that a smaller channel width/depth combination closer to the sensor’s diameter was best for the embedding process. After the desired parameters were selected, Type-K thermocouples were embedded and evaluated post-embedding using nondestructive thermal testing, as well as destructive sectioning and microscopy. Post-build characterization showed that the thermocouples were well-bonded to the SS316 matrix and were fully functional after embedding. During thermal testing to temperatures up to 500 °C, the embedded thermocouples read consistently with one another and deviated only slightly from the readings of a nonembedded thermocouple located within the furnace. This slight discrepancy was most likely due to differences in the thermal time constants for a nonembedded thermocouple vs. a thermocouple embedded in a solid SS316 block. The results presented in this report will serve as the foundation for future work that will focus on embedding sensors in relevant TCR reactor components and eventually testing those components under neutron irradiation.

36 MATERIALS SCIENCE↗

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗