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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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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Assessing pore network heterogeneity across multiple scales to inform CO2 injection models

Geologic heterogeneity is a key feature that must be considered when translations of scaled data are performed. This paper presents the assessment of geologic heterogeneity using a multiscale workflow that includes image analysis-based methods coupled with well log analysis to provide data in which fractals and machine learning methods estimate the carbon dioxide (CO 2 ) storage resource potential of a reservoir. The heterogeneity of rock properties of the complex Bell Creek reservoir in Montana, USA, was explored at the pore scale (~nm to mm), core scale (~mm to m), and well scale (~cm to m). The data used in this study included advanced image analysis of micro-CT (computed tomography) images (pore scale), thin sections (pore scale), plugs and core images (core scale) and well logs (well scale). The micro-CT images were segmented using a U-net segmentation approach into objects of pores and grains. Further, the segmented images were reconstructed into subvolumes of different sizes. Physical properties (porosity and permeability) and fractal dimensions were calculated for the various subvolumes, and Lorenz coefficient (Lc) values, a single parameter to describe the degree of heterogeneity within a pay zone section, were calculated from thin-section images and well logs. Porosity and fractal dimension values were used to estimate the 188-µm threshold of representative elementary volume (REV) in this study. Both the Lc and fractal dimension values were found to be negatively correlated. When these two parameters are combined, it is possible to discern differences in the complex porous networks of the samples analyzed in this study.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Understanding drivers of oil and gas well integrity issues in the greater wattenberg area of Colorado

Well integrity is critically important to maintain to minimize the environmental impacts of oil and gas development and other subsurface energy operations. The Wattenberg Field of Colorado—a top producing field with >40,000 wells—has one of the most robust publicly reported well integrity programs in the country. Here, in this study, we analyzed annular pressure and annular-fluid geochemical test results collected from Wattenberg wells through the end of 2019 to characterize the frequency and spatial variability of integrity issues in the field and understand their drivers. Estimated frequencies of integrity issues among tested wells were 8.2-17.1% between 1955 and 2019 and 6.1-11.4% in 2019 alone. The frequency of integrity issues was nearly four times greater in wells located above the Longmont Wrench Fault Zone. Potential drivers of integrity issues were identified using ensemble decision tree models trained with a broad set of relevant information. Models show that well integrity issues are spatially clustered on regional and sub-regional scales and suggest the relatively high frequency of integrity issues observed is likely attributed to geologic factors. These findings are valuable for regulatory agencies and operators seeking to inform well integrity monitoring, plugging, and emissions reduction efforts and design future subsurface energy projects.

03 NATURAL GAS↗
DOE OSTI2020

A thermally-limited bubble growth model for the relaxation time of superheated fuels

Here, we propose a novel approach to evaluate the relaxation time of vapor bubble growth in the context of the flash boiling of a superheated liquid. In alternative to the empirical correlation derived from superheated water experiments almost fifty years ago, the new model describes the thermally-dominated growth of vapor bubbles in terms that are dependent on the local Jakob number (the ratio of sensible heat to latent heat during phase change) and the number density of vapor bubbles. The model is tested by plugging the resulting relaxation time into the Homogenous Relaxation Model (HRM). Flash-boiling simulations carried out with HRM are compared with n-pentane (C 5 H 12 ) injection and boil-off experiments conducted with a real-size, axial-hole, transparent gasoline injector discharging into a constant-pressure vessel. The long-distance microscopy images from the experiments, processed to derive the projected liquid volume (PLV) of the spray, provide a unique set of time-resolved validation data for direct fuel injection simulations. At conditions ranging from flaring to mild and minimal flash boiling, we show that switching to the new relaxation time improves the agreement with the measured PLV profiles with respect to the standard empirical model. Particularly at flaring conditions, the predicted increase in gas cooling caused by rapid vapor production is shown to be more consistent with the observed boil-off.

42 ENGINEERING↗
DOE OSTI2021

Experimental investigation on the coolability of nuclear reactor debris beds using seawater

During the Fukushima nuclear reactor accident, seawater was injected into the reactor core to cool the decay heat from the heat generating porous debris bed. However, the impact of dissolved salts in water on the coolability of a debris bed is not well understood. This paper is one of the first works to investigate the cooling mechanisms for debris bed using seawater. An experimental system was built where the packed bed test section was volumetrically heated via a high frequency induction heater. The temperature along the axis of the test section was measured using a high resolution temperature sensor based on Optical Frequency Domain Reflectometry. Experimental results show that the dryout heat flux increases with an increase in concentration, with pure water having a dryout volumetric heat flux of 1.8 MW/m and salt water of concentration 7% having a dryout volumetric heat flux of 2.8 MW/m. However, this enhanced coolability using salt water is short term, as the crystallization fouling mechanism becomes significant over time and leads to gradual temperature excursion in the bed. The fouling mechanism eventually leads to a cross section of the debris bed to plug with the deposited salts, and this leads to a pressure build up in the lower regions of the debris bed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Validation of material models for puncture of 7075-T651 aluminum plate

Plate puncture simulations are challenging computational tasks that require advanced material models including high strain rate and thermal-mechanical effects on both deformation and failure, plus finite element techniques capable of representing large deformations and material failure. The focus of this work is on the material issues, which require large sets of experiments, flexible material models and challenging calibration procedures. In this study, we consider the puncture of 12.7 mm thick, 7075-T651 aluminum alloy plates by a cylindrical punch with a hemispherical nose and diameter of 12.7 mm. The plasticity and ductile failure models were isotropic with calibration data obtained from uniaxial tension tests at different temperatures and strain rates plus quasi-static notched tension tests and shear-dominated tests described here. Sixteen puncture experiments were conducted to identify the threshold penetration energy, mode of puncture and punch acceleration during impact, The punch was mounted on a 139 kg mass and dropped on the plates with different impact speeds. Since the mass was the same in all tests, the quantity of interest was the impact speed. The axis and velocity of the punch were perpendicular to the plate surface. The mean threshold punch speed was 3.05 m/s, and the mode of failure was plugging by thermal-mechanical shear banding accompanied by scabbing fragments. Application of the material models in simulations of the tests yielded accurate estimates of the threshold puncture speed and of the mode of failure. Time histories of the punch acceleration compared well between simulation and test. Remarkably, the success of the simulations occurred in spite of even the smallest element used being larger than the width of the shear bands.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Propagation method and planting density influence canopy developmental transition and biomass productivity in Miscanthus × giganteus

Understanding how establishment practices influence the mechanisms underlying Miscanthus × giganteus (miscanthus) productivity and canopy development is critical for optimizing management. Data was collected during the juvenile (2011–2013) and mature (2024) phases of a long-term field experiment established in Urbana, Illinois, to evaluate the effects of propagation method (plug propagation [PP] and rhizome propagation [RP]), planting density (1.0, 0.75, and 0.25 plants m⁻²), and nitrogen application (0 and 67 kg N ha⁻¹) on end-of-season biomass yield, tiller mass, tiller density, and tiller height. Linear regression models identified the dominant predictors of yield across stand ages and management regimes. Planting density, nitrogen (N) application, and propagation method significantly influenced early yield and canopy development. During the juvenile phase, biomass yield was driven by tiller density due to canopy expansion; in the mature phase, yield became driven by tiller mass. The PP plots produced higher tiller density than the RP plots, resulting in faster canopy closure and higher juvenile-phase yields. Rhizome-propagated (RP) plots produced lower tiller density, but individual tillers were 3.3–6.4 g tiller −1 heavier than PP tillers. After the canopy reached equilibrium, the PP and RP yields were similar because greater RP tiller mass compensated for its lower tiller density. Higher planting density resulted in greater yield and tiller density during the second year (2012), but this effect was absent from the third year (2013) onward. In the juvenile phase, N fertilization enhanced yield by 1.6–3.4 Mg ha −1 . Initiating fertilization in 2013 on unfertilized plots produced biomass similar to that in fertilized plots, suggesting yield recovery in the mature phase. These findings revealed that establishment strategies, including propagation method and planting density, influence juvenile miscanthus canopy development and productivity, transitioning from tiller-density- to mass-dominated yields, but not mature phase productivity.

09 BIOMASS FUELS↗
DOE OSTI2022

Quantifying policy gaps for achieving the net-zero GHG emissions target in the U.S. light-duty vehicle market through electrification

The U.S. light-duty vehicle (LDV) industry, a major greenhouse gas (GHG) emitting sector, is embracing decarbonization. Considering only electrification pathways, this study uses publicly-available tools – MA3T and VISION on vehicle market penetration, fleet accounting and life-cycle analysis to quantify the policy gaps for LDVs to achieve the net-zero GHG emissions target in nine vehicle penetration cases under two electricity mix scenarios, including the U.S. administration's decarbonization strategy – 100% clean electricity by 2035. The MA3T model is a multinomial discrete choice model for market share projection by vehicle technology, and the VISION is a vehicle stocks and GHG emissions projection model by using vehicle and travel characteristics. This study projects the impacts of technology and policy enforcement on shaping the dynamics and decarbonization of the LDV market. Additionally, achieving the expected improvement of battery technology and charging infrastructure is critical but can only reduce the 2050 GHG emissions to 48–54% of the 2020 level under the electricity renewable mix scenario. It is almost impossible to achieve a 100% battery electric vehicle stock by 2050 and the 2050 net-zero target in the LDV industry unless ban of internal combustion engine technology is implemented starting in 2035 and under the 2035 100% clean electricity scenario. These extreme conditions also sacrifice most from the consumer welfare perspective. A greater policy forcing intensity accelerates plug-in electric vehicle penetration, while with declining marginal effect and reduced consumer welfare. Among the investigated policy scenarios, the policy forcing intensity equivalent to a fuel tax of $1–2 per gasoline gallon reduces the most GHG emissions while keeping a positive consumer welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks. We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. Furthermore, the DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a “plug-and-play” mode.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stress characterization for friction-stir-welded electric vehicle battery trays with application of neutron diffraction

The battery tray is an essential component that protects and controls battery-cell temperatures in electric and plug-in hybrid vehicles. The functional stress limit of the battery tray heavily depends on the residual stress acquired from the manufacturing process. Consequently, exceeding the stress limit of the battery tray during operation could compromise the battery-cell banks and may risk the vehicle's safety. Hence, understanding residual stress formation is vital for design and safety concerns. Here, in the current study, AA 6061-plates were friction stir welded to an A365 high-pressure die-cast battery tray to create sealed coolant channels in the battery tray. However, this multi-material lap friction stir weld introduces residual stress into the battery tray, resulting in distortion. This distortion was mitigated using burnishing or coining operations, though straightening the battery tray had initially unknown effects on the residual stress. Therefore, neutron diffraction was utilized to characterize residual stresses after straightening. The results indicate that the friction stir welding (FSW) operation generated residual stresses exceeding the yield strength of the material, consequently deforming the battery tray by ±3 mm from the pre-weld geometry. The burnishing operation reduced the residual stresses below the material's yield strength while restoring the tray to within ±0.75 mm of the pre-weld geometry. Similarly, the coining operation restored the battery tray to within ±0.75 mm of the pre-weld geometry, however, increasing the number of locations where the residual stress exceeds the yield strength of the material.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Analysis of time-dependent strain heterogeneity in shales using X-ray microscopy and digital volume correlation

In this paper, we report the results of a 4-dimensional (3 spatial dimensions plus time) in-situ creep experiment on a milli-core shale plug from Barnett formation in Texas. An outstanding challenge in shale mechanics is connecting observable characteristics to predictable mechanical and hydraulic behavior. We employ novel imaging and analysis techniques to statistically link sample mineralogy and structure to observed deformation. In particular, we focus on mechanisms of porosity reduction during transient response to step changes in stress, analogous to the aseismic deformation that occurs after an episode of fracturing. Our main goal in this study is to take the first steps to visualize and capture the small-scale deformation mechanisms involved in creep of shales, using imaging techniques. To do so, we conducted a uniaxial creep experiment inside an Xradia Versa 520 micro-CT system for 12 h at room temperature under a constant uniaxial stress of 25 MPa. We employed a Digital Volume Correlation (DVC) method to measure micro-scale deforspmation of the sample by comparing the resulting volumetric images with a high-resolution scan of the sample obtained prior to the creep experiment. The results indicate that the time-dependent deformation in the compliant clay plus kerogen matrix constituents facilitates rigid grain rotation and compaction of intergranular porosity at the boundary between rigid grains and matrix.

58 GEOSCIENCES↗
DOE OSTI2020

X-ray and gamma-ray tomographic imaging of fuel relocation inside sodium fast reactor test assemblies during severe accidents

The present work reports on x-ray and gamma-ray high-spatial resolution computerized tomography measurements of the Pin Bundle Metallic Fuel Relocation (PBR) assemblies tested in the Metallic Uranium Safety Experiment (MUSE) facility at Argonne National Lab (ANL). The aim of the study was to characterize fuel relocation structures that develop during severe core accidents pertaining to SFR assemblies; these include but are not limited to advanced core disruption recreated in the PBR-1 assembly, and cladding breach recreated in the PBR-2 assembly. We report the x-ray tomography measurements were able to resolve small quantities of relocation fuel; with increased presence of relocation fuel, the x-ray 1measurements spatially mapped the material but could not resolve the inner regions of these. The gamma-tomography measurements showed improved results, resolving the relocation structures in great detail. The upper plenum of the PBR-1 assembly where the molten uranium was initially inserted presented high structural damage, reflected by the partial and complete disintegration of the central rods. Relocation fuel filled the subchannels, adhering to surviving cladding walls and the assembly casing. In the lower portion of the measured section, the tomogram degrades due to photon starvation effects hinting at the increased amount of relocation fuel potentially plugging the assembly; flow blockage in this section was difficult to determine due to the tomogram’s degradation from photon starvation. Small fragments were observed further down the assembly, dislodged from the initial insertion of the molten material. This section was used as an unperturbed assembly reference, with a calculated blockage of less than 1% from the present fragments. The PBR-2 assembly was characterized by columnar relocation structures propagating through the subchannels. Three of the relocation structures were captured in the measured section, with evidence of cross migration on to adjacent subchannels. The measured section in this assembly captures the leading edge of two structures. The calculated flow blockage was 16% in the planes where the three relocation structures are present, but this quickly decreases to approximately 5% past the leading edge of two of the structures.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

The response of accident tolerant fuel cladding to LOCA burst testing: A comparative study of leading concepts

Accident tolerant fuel claddings seek to improve safety margins during loss-of-coolant accident (LOCA) scenarios by reducing cladding steam oxidation rates, hydrogen production, delaying or mitigating cladding burst, and reducing cladding deformation. After rapid and extensive progress in recent years, Cr coated Zr-based alloys, ferritic FeCrAl, and SiC/SiC ceramic matrix composites (CMCs) have emerged as the most promising cladding concepts, but there are few studies comparing the accident tolerance of all three concepts simultaneously. Here, in this study, LOCA burst testing has been conducted on Cr high impulse power magnetron sputtered Zry-4 (Cr/Zry-4), C26M (FeCrAl), and SiC/SiC SiGA (CMC). Experimental observations indicate Cr/Zry-4 burst at higher temperatures than Zry-4 however the effectiveness of the coating on mitigating ZrO 2 formation via Cr 2 O 3 formation depended on physical proximity to the burst opening. No dramatic improvement in diametrical strain nor opening geometry was observed. C26M burst at higher temperatures than Zry-4 at lower pressures, exhibiting small amounts of strain and smaller openings, and formed slow-growing Al 2 O 3 regardless of location. The CMCs did not burst or show any macroscopic signs of deformation, all the way up to an internal cladding pressure of 15.2 MPa. High temperature expanding Nb plug testing indicated that CMC room temperature strength may persist up to 1650°C, with an approximately 40% loss of strength at 1900°C. CMC steam oxidation was also compared to reference chemically vapor deposited SiC up to 1700°C, and CMCs were found to oxidize at slightly accelerated rates that were still orders of magnitude lower than bare Zry-4. Projected H 2 generation during LOCA burst testing showed that when accounting for cladding burst exposing inner diameters to steam, Cr coated Zry-4 reduced H 2 generation by a factor of two compared with bare Zry-4, while both C26M and SiC/SiC reduced H 2 generation by orders of magnitude relative to bare Zry-4.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Spatial heterogeneity analyses of pore structure and mineral composition of Barnett Shale using X-ray scattering techniques

The spatial heterogeneity of pore structure and mineral composition at mu m to mm scales in mm to cm-sized shale samples complicates the laboratory measurements of porosity & pore size distribution and consequently reservoir quality evaluation. Traditional fluid invasion characterization methods typically take hours to days to get data and can only test relatively small samples (usually 2.54 cm diameter core plugs and mm-sized rock chips). Furthermore, the Xray scattering techniques at the Advanced Photon Source of the Argonne National Laboratory have the capability to non-destructively determine the pore structure and mineral composition of mm x mm area in a short time of seconds and to hold several to hundreds of mm 2 sized sample to conduct large area heterogeneity analysis in the short duration of hours. With the use of ultra-small angle X-ray scattering (USAXS), small-angle X-ray scattering (SAXS), and wide-angle X-ray scattering (WAXS), the porosity, surface area and pore size distribution of two Barnett Shale samples have been mapped out and the mineral compositions are determined qualitatively. Overall, the porosity and pore surface area of the Barnett Shale Sample A over a 36 cm2 area ranges from 1.70 % to 8.13 % and 8.87 m 2 /g to 40.2 m 2 /g respectively. The porosity and surface area of Sample B over a 24 cm 2 area varies from 3.15 % to 11.7 % and 18.3 m 2 /g to 60.2 m 2 /g. In Sample A, the mineral composition shows a shift from carbonate-rich to siliciclastic-rich over a distance of several millimeters. For Sample B, the mineral compositions are mainly siliciclastic and do not show an obvious lithological change. The direct observations of high spatial heterogeneity of pore structure and mineral composition in shale illustrate the utility of integrated X-ray scattering techniques to provide valuable insights into shale studies and reservoir evaluation.

58 GEOSCIENCES↗
DOE OSTI2022

Oxidative coupling of methane (OCM) conversion into C 2 products through a CO 2 /O 2 co-transport membrane reactor

Oxidative coupling of methane (OCM), which transforms CH 4 into C 2 products (C 2 H 6 and C 2 H 4 ) with molecular O 2 as the oxidant, is one of the most studied direct methane conversions (DMCs). However, a major technical hurdle to the OCM process is to achieve high CH 4 conversion at high C 2 (C 2 H 6 and C 2 H 4 ) selectivity. One rudimentary cause for this “tradeoff” behavior is the high chemical reactivity of the products (C 2 H 6 or C 2 H 4 ), which can be re-oxidized by O 2 . To overcome this thermodynamic challenge, minimizing the oxidizing power of the oxidant and lowering the local oxygen partial pressure are keys. Here, In this work, we demonstrate a new membrane reactor that capture CO 2 /O 2 from a flue gas and uses it for OCM conversion. The results show that the co-captured CO 2 /O 2 mixture converts CH 4 into C 2 H 6 in the presence of a 2%Mn–5%Na 2 WO 4 /SiO 2 catalyst, followed by thermal cracking of C 2 H 6 into C 2 H 4 and H 2 . The presence of CO 2 decreases the local partial pressure of O 2 , thus reducing the propensity of C 2 -products re-oxidation and leading to a higher C 2 selectivity. We show that a small button-type membrane reactor can achieve 12% C 2 yield with ~57% C 2 -selectivity using a diluted CH 4 -Ar mixture as the feedstock. We expect higher C 2 yield with tubular plug-flow membrane reactors in the future. We also highlight the unique advantage of the membrane reactor in intensifying CO 2 capture from both flue gas and OCM purification process into one single step.

42 ENGINEERING↗
DOE OSTI2022

Effect of a nanoparticle on wettability alteration and wettability retainment of carbonate reservoirs

The oil recovery in many carbonate reservoirs is low due to oil-wetness and heterogeneity. In this study, nanoparticles are evaluated for altering the wettability of oil-wet limestones and their properties are compared with those of an anionic surfactant. A surface-modified silica nanoparticle (SiNP) with a negative zeta potential was found to be aqueous stable in brines. Wettability studies showed that the SiNP cannot change the wettability of an initially oil-wet calcite plate, but SiNP treated calcite surface can remain water-wet after aging in oil. Spontaneous imbibition tests confirmed the observations of wettability tests and showed that a SiNP treated carbonate core retained its water-wettability during oil injection and aging. The imbibition into a SiNP treated and oil aged core was comparable to that in a water-wet core. However, SiNP was not able to remove the oil layers in initially oil-wet cores and imbibe water into these cores. In contrast, the anionic surfactant could alter the oil-wet carbonate rocks to a more water-wet condition, but failed to prevent the water-wet surface from getting oil-wet during oil-aging. The results suggest that the SiNP can be injected into wettability-altered (water-wet) reservoirs/regions to help retain the water-wettability during the long-term oil production. The 0.5 wt% SiNP dispersions transported through 18 mD limestone cores without any plugging. The SiNP retention was measured to be 2.5 mg/m 2 , much higher than that of the anionic surfactant.

02 PETROLEUM↗
DOE OSTI2023

Direct measurement and calculation of rubber bulk modulus by piston-cylinder method using conventional mechanical testing equipment

This article describes a method to directly measure the bulk modulus of rubber using a piston-cylinder type apparatus. The function of the testing apparatus is to reliably transfer load to the water inside the vessel and allow for the accurate and continuous measurement of volumetric displacement as the contents are compressed. During the test, load is applied to a piston-cylinder containing the rubber test sample and water using a conventional mechanical testing load frame. Load and the travel of the piston are recorded by a load cell and extensometer, respectfully. A brass or stainless steel plug of the same dimensions as the test sample is tested as a control sample to isolate the compliance of the system, including the compressibility of water and compliance of the piston-cylinder. The results from this control test are used to disincorporate the compliance of the system from the sample test results. Load-linear displacement data are mathematically converted to pressure-volumetric displacement data, from which bulk modulus is calculated. The test apparatus and method are validated using the known bulk modulus of water. Finally, the bulk modulus for two similar rubbers is evaluated. The validity of the results and limitations of the device are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The MOOSE electromagnetics module

The Multiphysics Object-Oriented Simulation Environment (MOOSE) electromagnetics module has been developed to increase MOOSE physics module capabilities, enabling standalone and coupled computational electromagnetics within the MOOSE multiphysics ecosystem. The module is actively being utilized in the areas of plasma physics and advanced manufacturing, and it currently provides initial demonstrated capability in multi-dimensional, complex-valued electromagnetic wave propagation, electrostatic contact, reflection and transmission, and electromagnetic eigenvalue problems. Two-dimensional wave propagation and one-dimensional wave reflection and transmission are showcased as examples in this work. The modularity, parallelism, and plug-in infrastructure for custom future development is inherited from MOOSE itself, and the module can be used with both MOOSE-based and external codes, giving great flexibility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗