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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 1,207 records · Page 67

All sources NASA NTRS DOE OSTI

NASA NTRS2001

Glenn-HT: The NASA Glenn Research Center General Multi-Block Navier-Stokes Heat Transfer Code

For the last several years, Glenn-HT, a three-dimensional (3D) Computational Fluid Dynamics (CFD) computer code for the analysis of gas turbine flow and convective heat transfer has been evolving at the NASA Glenn Research Center. The code is unique in the ability to give a highly detailed representation of the flow field very close to solid surfaces in order to get accurate representation of fluid heat transfer and viscous shear stresses. The code has been validated and used extensively for both internal cooling passage flow and for hot gas path flows, including detailed film cooling calculations and complex tip clearance gap flow and heat transfer. In its current form, this code has a multiblock grid capability and has been validated for a number of turbine configurations. The code has been developed and used primarily as a research tool, but it can be useful for detailed design analysis. In this paper, the code is described and examples of its validation and use for complex flow calculations are presented, emphasizing the applicability to turbomachinery for space launch vehicle propulsion systems.

Gaugler, Raymond E.↗

NASA NTRS2002

Glenn-HT: The NASA Glenn Research Center General Multi-Block Navier-Stokes Heat Transfer Code

For the last several years, Glenn-HT, a three-dimensional (3D) Computational Fluid Dynamics (CFD) computer code for the analysis of gas turbine flow and convective heat transfer has been evolving at the NASA Glenn Research Center. The code is unique in the ability to give a highly detailed representation of the flow field very close to solid surfaces in order to get accurate representation of fluid heat transfer and viscous shear stresses. The code has been validated and used extensively for both internal cooling passage flow and for hot gas path flows, including detailed film cooling calculations and complex tip clearance gap flow and heat transfer. In its current form, this code has a multiblock grid capability and has been validated for a number of turbine configurations. The code has been developed and used primarily as a research tool, but it can be useful for detailed design analysis. In this presentation, the code is described and examples of its validation and use for complex flow calculations are presented, emphasizing the applicability to turbomachinery.

Gaugfer, Raymond E.↗

DOE OSTI2020

NMDQi Thermal-hydraulic Optimization, Analysis, and Scoping Tool (TOAST)

The Thermal-hydraulic Optimization, Analysis, and Scoping Tool (TOAST) is developed to support the thermal-hydraulic aspects for the design of optimal irradiation vehicles for the Nuclear Materials Discovery and Qualification initiative (NMDQi). TOAST is currently a MATLAB-based tool that utilizes a simplified steady-state analytical model where a radial thermal resistance circuit is utilized to account for conduction through up to 2 capsules, a gas gap, a thermal bond, a sample cladding, and a sample, as well as the convection from a water coolant outside the capsules. The geometry is discretized axially along the user-defined height of a basket with a user-defined number of points/nodes, essentially turning TOAST into a semi-2D heat transfer analysis utility for cylindrical irradiation vehicles with practically any configuration, solving for temperatures radially at multiple axial locations. TOAST utilizes a Graphical User Interface (GUI) in-which a user can define the geometrical layout, the materials utilized for each component, the coolant characteristics, and the required solution. The user can define the geometry by inputting the diameters, thicknesses, and heights for each component, whereas the materials are defined via the user-provided constant or variable thermal conductivities. The user can select the coolant's inlet temperature, pressure, and the pressure drop across the height of the problem (which is used to calculate the velocity of the flow). Finally, the user can choose to solve for a sample heat generation rate limit by inputting temperature limits for the sample and capsules or can choose to purely solve for the axial temperature distributions of each component by inputting a pre-selected heat generation rate. Either way, TOAST provides the user with axial temperature distributions of all the components including the coolant, and the heat generation rate limit as well as the maximum outlet coolant temperature. The user can also choose to do one of 6 sensitivity analyses in TOAST. The sensitivity analyses yield plots of the sensitivity of the heat generation rate limit, the maximum coolant temperature, and the pressure limit for the annular components due to perturbations in 1-2 unknown variables based on the selected sensitivity analysis. Benchmarks between computations in TOAST and equivalent 2D axis symmetric ABAQUS models are presented, showing that TOAST results are within less than 3% of ABAQUS results in most cases, and a maximum of 8% difference in some cases. The benchmarks also revealed that this uncertainty is tied to the selection of an appropriate Nusselt number correlation and appropriate thermal conductivities, which the user can do from the GUI. Regardless, TOAST is demonstrated as a computationally efficient, highly accessible, and accurate utility for optimization and scoping s of studies different irradiation vehicles.

42 ENGINEERING↗

DOE OSTI2021

Mechanical Loads on Spent Nuclear Fuel in the General 30 cm Package Drop Scenario

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) Spent Fuel and Waste Science & Technology (SFWST) research program is guided by the high-level goal of closing prioritized knowledge gaps related to spent nuclear fuel (SNF) storage and transportation, which are summarized by Saltzstein et al. (2020). One of the high-priority knowledge gaps is the identification and quantification of mechanical loads that are expected to affect SNF during normal conditions of transportation and storage to inform the range of physical SNF test programs. This report uses modeling and analysis methods to estimate the mechanical loads on spent nuclear fuel (SNF) in the general 30 cm package drop scenario. The drop scenario assumes impact limiters are in place in the transportation configuration and the impact surface is perfectly rigid. The goal of this analysis is to consider the universe of potential mechanical loading conditions that can happen to SNF and present the results in a manner that is useful for materials testing, decision making, and regulatory rule making purposes. This study uses validated finite element models and methods to perform a broad parametric study of key variables that can affect the mechanical loads on SNF during a hypothetical package free drop scenario. Physical drop test data from a cask and fuel assembly drop test campaign is the basis for model validation. Additionally, the results of the parametric study are used to inform a damage model, which uses multiple nonlinear regression to estimate the relationships between input variables and output response. The parametric finite element analyses consider thousands of input variable combinations, while the damage model estimates millions of combinations. The breadth of this study provides confidence that the potential range of mechanical loads that SNF might experience during the general 30 cm package drop scenario are characterized well enough to consider this knowledge gap closed. While this report documents the overall peak values calculated in this study, the 95 th percentile values, the histograms, and the observed trends are equally important. This study covered a large range of SNF temperatures, room temperature to 300°C, and burnups, 10 GWd/MTU to 62 GWd/MTU. Each temperature and burnup combination has a different cladding yield strain, so it is more meaningful to summarize the calculated cladding strain response as its factor of safety, which is defined relative to the yield strain. The factor of safety is calculated as the yield strain divided by the peak cladding strain. A factor of safety greater than unity indicates that the cladding remains below yield, whereas a value less than unity is indicative of plastic deformation. In all cases of this study a safety factor over 1.0 was calculated, although in the most limiting case at 300°C the safety factor was only 1.01, which suggests that yielding could occur when additional loads like rod internal pressure are included. When the temperature is restricted to 200°C the limiting safety factor increases to 1.28, which has significant margin to accommodate internal pressure and potential local cladding defects that could cause a local stress concentration. An important trend in the calculated fuel rod mechanical loads is that the 2 nd highest loaded fuel rod in an assembly tends to be significantly lower than the highest loaded rod. The implication is that even if one rod in an assembly experiences a failure the loads would have to be significantly higher to cause two or more rods to fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Sifting for a Stream: The Morphology of the $300S$ Stellar Stream

Stellar streams are sensitive laboratories for understanding the small-scale structure in our Galaxy’s gravitational field. Here, we analyze the morphology of the $300S$ stellar stream, which has an eccentric, retrograde orbit and thus could be an especially powerful probe of both baryonic and dark substructures within the Milky Way. Due to extensive background contamination from the Sagittarius stream (Sgr), we perform an analysis combining Dark Energy Camera Legacy Survey photometry, $Gaia$ DR3 proper motions, and spectroscopy from the Southern Stellar Stream Spectroscopic Survey (S 5 ). We redetermine the stream coordinate system and distance gradient, then apply two approaches to describe $300S$ ’s morphology. In the first, we analyze stars from $Gaia$ using proper motions to remove Sgr. In the second, we generate a simultaneous model of $300S$ and Sgr based purely on photometric information. Both approaches agree within their respective domains and describe the stream over a region spanning 33° . Overall, $300S$ has three well-defined density peaks and smooth variations in stream width. Furthermore, $300S$ has a possible gap of ~4.7 and a kink. Dynamical modeling of the kink implies that $300S$ was dramatically influenced by the Large Magellanic Cloud. This is the first model of $300S$ ’s morphology across its entire known footprint, opening the door for deeper analysis to constrain the structures of the Milky Way.

Milky Way galaxy↗

DOE OSTI2024

Review of data-driven models for quantifying load shed by non-residential buildings in the United States

Shifting and shedding power demand in buildings can be cost-effective techniques for grids to function reliably and for end users to earn compensation. Grid operators reimburse customers in proportion to the quantity of load shed. Simple data-driven methods are used to quantify this shed, which is the difference between a measured load during the event and modeled "baseline" that would have occurred in absence of the event. These methods have evolved over the years and in many cases have been integrated with building physics, to make them a hybrid between physics based and empirical models. However, there is no comprehensive analysis that provides guidance to building operators, grid operators and researchers in selecting appropriate models based on their specific needs and available data. Here, this work aims to fill this gap by critically assessing the performance of baseline models put forward from the year 2000 through 2023. The literature reviewed includes reports generated by grid operators, reports from national laboratories and academic journal articles. The work outlines modeling features like the inputs, training period, estimation method, adjustments to fine tune the predictions and metrics to evaluate the performance. A comprehensive list of 50 models has been provided. For each model, the study explores the applicability of the model to weather sensitive buildings, variability in the building profile, timing of the event, and whether the building reduces energy consumption before an event. The work identifies the situations in which a particular model works and draws lessons based on evidence of performance. Finally, recommendations to aid in model selection are given.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Investigations on the Origin of Topotactic Phase Transition of LaCoO 3 Thin Films with In Situ XRD and Ambient Pressure Hard X-ray Photoelectron Spectroscopy

With the applications of in situ X-ray diffraction (XRD), electrical I–V measurement, and ambient pressure hard X-ray photoelectron spectroscopy (AP-HAXPES), the characteristics of the topotactic phase transition of LaCoO 3 (LCO) thin films are examined. XRD measurements show clear evidence of structural phase transition (SPT) of the LCO thin films from the perovskite (PV) LaCoO 3 to the brownmillerite (BM) La 2 Co 2 O 5 phases through the intermediate La 3 Co 3 O 8 phase at a temperature of 350 °C under high-vacuum conditions, ~10 –5 mbar. The reverse SPT from BM to PV phases is also found under ambient pressure (>100 mbar) of air near 100 °C. Both observed SPTs in XRD are also identified in the electrical I–V measurements, i.e., the metallic PV phase to the insulating BM phase and vice versa. During the onset of SPTs, the bulk chemical and electronic states of LCO thin films are monitored with AP-HAXPES. The oxidation states in Co 2p spectra indicate that the oxygen vacancies are closely related to the SPT of LCO thin films. Also, the presence of enlarged band gap is observed as the SPT from PV to BM phases takes place, revealing the modified electronic properties of LCO due to the creation of oxygen vacancies. In conclusion, the analysis of valence band structures is further compared to the I–V measurements.

36 MATERIALS SCIENCE↗

DOE OSTI2023

The transition from field emission to collisional space-charge limited current with nonzero initial velocity

Abstract Multiple electron emission mechanisms often contribute in electron devices, motivating theoretical studies characterizing the transitions between them. Previous studies unified thermionic and field emission, defined by the Richardson-Laue-Dushman (RLD) and Fowler–Nordheim (FN) equations, respectively, with the Child-Langmuir (CL) law for vacuum space-charge limited current (SCLC); another study unified FN and CL with the Mott-Gurney (MG) law for collisional SCLC. However, thermionic emission, which introduces a nonzero injection velocity, may also occur in gas, motivating this analysis to unify RLD, FN, CL, and MG. We exactly calculate the current density as a function of applied voltage over a range of injection velocity (i.e., temperature), mobility, and gap distance. This exact solution approaches RLD, FN, and generalized CL (GCL) and MG (GMG) for nonzero injection velocity under appropriate limits. For nonzero initial velocity, GMG approaches zero for sufficiently small applied voltage and mobility, making these gaps always space-charge limited by either GMG at low voltage or GCL at high voltage. The third-order nexus between FN, GMG, and GCL changes negligibly from the zero initial velocity calculation over ten orders of magnitude of applied voltage. These results provide a closed form solution for GMG and guidance on thermionic emission in a collisional gap.

42 ENGINEERING↗

DOE OSTI2022

Superconducting properties of the spin Hall candidate Ta 3 Sb with eightfold degeneracy

We report the synthesis and characterization of phase pure Ta 3 Sb, a material predicted to be topological with eightfold degenerate fermionic states [Bradlyn et al., Science 353, aaf5037 (2016)] and to exhibit a large spin Hall effect [Derunova et al., Sci. Adv. 5, eaav8575 (2019)]. We observe superconductivity in Ta 3 Sb with T c ~0.67 K in both electrical resistivity ρ(T) and specific heat c(T) measurements. Field-dependent measurements yield the superconducting phase diagram with an upper critical field of H c2 (0) ~0.95 T, corresponding to a superconducting coherence length of ξ ≈ 18.6 nm. The gap ratio deduced from specific heat anomaly, 2Δ 0 /k B T c is 3.46, a value close to the Bardeen-Cooper-Schrieffer value of 3.53. From a detailed analysis of both the transport and thermodynamic data within the Ginsburg-Landau (GL) framework, a GL parameter of κ ≈ 90 is obtained, identifying Ta 3 Sb as an extreme type-II superconductor. The observation of superconductivity in an eightfold degenerate fermionic compound with topological surface states and predicted large spin Hall conductance positions Ta 3 Sb as an appealing platform to further explore exotic quantum states in multifold degenerate systems.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Electronic structure of the frustrated diamond lattice magnet NiRh 2 O 4

We report the A -site spinel NiRh 2 O 4 is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here we carry out resonant inelastic x-ray scattering (RIXS), x-ray absorption spectroscopy (XAS), and inelastic neutron scattering (INS) to characterize the local electronic structure and lattice dynamics of NiRh 2 O 4 . The RIXS data can be partly described by a single-ion model for tetrahedrally coordinated Ni 2+ and indicates a tetragonal distortion Δt 2 = 70 meV that splits the t 2 orbitals into a high energy orbital singlet and lower energy orbital doublet. We identify features of the RIXS spectra that are consistent with a Rh-Ni two-site excitation indicating strong metal-metal hybridization mediated by oxygen in NiRh 2 O 4 . We also identify signatures of electron-phonon coupling through the appearance of phonon sidebands that dress crystal field excitations. These results establish the key energy scales relevant to the magnetism in NiRh 2 O 4 and further demonstrate that covalency and lattice dynamics play essential roles in controlling the magnetic ground states of A -site spinels.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Electron– K -phonon interaction in twisted bilayer graphene

We develop an analytic theory to describe the interaction between electrons and K phonons and study its influence on superconductivity in the bare bands of twisted bilayer graphene (TBG). We find that, due to symmetry and the two-center approximation, only one optical K phonon (160meV) of graphene is responsible for the intervalley electron-phonon interaction. Here, this phonon has recently been found in angular-resolved photoemission spectroscopy to be responsible for replicas of the TBG flat bands. By projecting the interaction to the TBG flat bands, we perform the full symmetry analysis of the phonon-mediated attractive interaction and pairing channels in the Chern basis, and show that several channels are guaranteed to have gapless order parameters. From the linearized gap equations, we find that the highest T c pairing induced by this phonon is a singlet gapped s-wave inter-Chern-band order parameter, followed closely by a gapless nematic d-wave intra-Chern-band order parameter. We justify these results analytically, using the topological heavy-fermion mapping of TBG which has allowed us to obtain an analytic form of a phonon-mediated attractive interaction and to analytically solve the linearized and T = 0 gap equations. For the intra-Chern-band channel, the nematic state with nodes is shown to be stabilized in the chiral flat-band limit. While the flat-band Coulomb interaction can be screened sufficiently enough—around the Van Hove singularities—to allow for electron-phonon based superconductivity, it is unlikely that this effect can be maintained in the lower density of states excitation bands around the correlated insulator states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Mapping Rydberg States of H 2 with the Halfium R-Matrix Method

In this article, we use the Halfium R-matrix method to investigate the Rydberg states of the H 2 molecule up to n = 20, filling the gap above the low-lying bound states already calculated with configuration interaction packages. Moreover, we show that the use of Quantum Defect Theory scaling laws, allows for a comprehensive analysis of the regular patterns resulting from the coupling between Rydberg series and doubly excited states. The results should open the door for more efficient quasi-diabatization of the potential energy curves which is required for calculating cross sections and rate coefficients of the (e + H 2 + ) collisional processes, involved in the plasma modeling for fusion devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Defensive Cybersecurity Architecture Design Using Force-on-Force Cyber-Physical Modeling

Currently, nuclear power plant physical security systems are highly dependent on air-gaps as a protective measure against cyber-threats. Cyber-physical threats become more likely as advanced cyber-threat capabilities to jump air-gaps transition into common use. Defending against the emerging threat of cyber-enabled physical intrusions is poorly understood. The consequence of these cyber-physical attacks has no quantitative analysis method to inform risk-informed, performance-based cybersecurity approaches. By modifying the physical security simulation tool Dante, cyber-physical threat consequence was able to be analyzed on a notional facility. The results of this analysis are used to design a Defensive Cybersecurity Architecture (DCSA) for the physical security system to produce example resilience measures for this notional facility. A DCSA defines security levels to provide a graded approach for defending plant functions, and security zones for trusted communication between systems. This approach can be applied to real world systems to produce physical protection systems and response measures that are resilient to cyber-physical threats.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2024

Droplet Entrainment in Steam Supply System of Water-Cooled Small Modular Reactors: Experiment and Modeling Approaches

Droplet entrainment in steam-flow is a prominent phenomenon that needs adequate safety and risk analysis of postulated transient and accident scenarios—including experimental investigation and representative modeling and simulation (M&S)—for small modular reactor (SMR) system design and demonstration. This study identifies knowledge gaps by evaluating experimental and computational fluid dynamics modeling approaches to support early-stage reactor system design, testing, and model evaluation. Previous studies reported in the literature for steam-flow entrainment primarily focused on gigawatt capacity pressurized water reactor (PWR) systems. However, entrainment phenomena are even more prominent for PWR-type SMRs due to their more compact integrated designs, which need further research and development. To fill the research gaps, this study provides insight by specifying the phenomena of interest by leveraging the lessons learned from past research, adopting advanced M&S techniques and advanced instrumentation and control. The findings and recommendations are applicable for evaluating steam-flow entrainment models and for designing integral effect test and separate effect test facilities for gaining reactor design approvals.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Considerations for Optimizing the Photometric Classification of Supernovae from the Rubin Observatory

The Vera C. Rubin Observatory will increase the number of observed supernovae (SNe) by an order of magnitude; however, it is impossible to spectroscopically confirm the class for all SNe discovered. Thus, photometric classification is crucial, but its accuracy depends on the not-yet-finalized observing strategy of Rubin Observatory's Legacy Survey of Space and Time (LSST). We quantitatively analyze the impact of the LSST observing strategy on SNe classification using simulated multiband light curves from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC). First, we augment the simulated training set to be representative of the photometric redshift distribution per SNe class, the cadence of observations, and the flux uncertainty distribution of the test set. Then we build a classifier using the photometric transient classification library snmachine, based on wavelet features obtained from Gaussian process fits, yielding a similar performance to the winning PLAsTiCC entry. We study the classification performance for SNe with different properties within a single simulated observing strategy. We find that season length is important, with light curves of 150 days yielding the highest performance. Cadence also has an important impact on SNe classification; events with median inter-night gap <3.5 days yield higher classification performance. Interestingly, we find that large gaps (>10 days) in light-curve observations do not impact performance if sufficient observations are available on either side, due to the effectiveness of the Gaussian process interpolation. This analysis is the first exploration of the impact of observing strategy on photometric SN classification with LSST.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2000

Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells

The results of an experimental and numerical study of the effects of imperfections on the buckling response of unstiffened thin-walled composite cylindrical shells are presented. Results that identify the individual and combined effects of traditional initial geometric shell-wall imperfections and non-traditional shell-wall thickness variations, shell-end geometric imperfections and variations in loads applied to the ends of the shells on the shell buckling response are included. In addition, results illustrating the effects of manufacturing flaws in the form of gaps between adjacent pieces of graphite-epoxy tape in some of the laminate plies are presented in detail. The shells have been analyzed with a nonlinear finite-element analysis code that accurately accounts for these effects on the buckling and nonlinear responses of the shells. The numerical results indicate that traditional and nontraditional initial imperfections can cause a significant reduction in the buckling load of a compression-loaded composite shell. Furthermore, the results indicate that the imperfections couple in a nonlinear manner. The numerical results correlate well with the experimental results. The nonlinear analysis results are also compared to the results from a traditional linear bifurcation buckling analysis. The results suggest that the nonlinear analysis procedure can be used for determining accurate, high-fidelity design knockdown factors for shell buckling and collapse. The results can also be used to determine the effects of manufacturing tolerances on the buckling response of composite shells.

Hilburger, Mark W.↗

NASA NTRS2015

Applied Operations Research: Augmented Reality in an Industrial Environment

Augmented reality is the application of computer generated data or graphics onto a real world view. Its use provides the operator additional information or a heightened situational awareness. While advancements have been made in automation and diagnostics of high value critical equipment to improve readiness, reliability and maintenance, the need for assisting and support to Operations and Maintenance staff persists. AR can improve the human machine interface where computer capabilities maximize the human experience and analysis capabilities. NASA operates multiple facilities with complex ground based HVCE in support of national aerodynamics and space exploration, and the need exists to improve operational support and close a gap related to capability sustainment where key and experienced staff consistently rotate work assignments and reach their expiration of term of service. The initiation of an AR capability to augment and improve human abilities and training experience in the industrial environment requires planning and establishment of a goal and objectives for the systems and specific applications. This paper explored use of AR in support of Operation staff in real time operation of HVCE and its maintenance. The results identified include identification of specific goal and objectives, challenges related to availability and computer system infrastructure.

Cole, Stuart K.↗

DOE OSTI2020

Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems

A robust, sufficiently accurate and practical hydrodynamic simulation toolset is required as a key component of the modeling and simulation of air-gap electrostatic discharge events. This work was performed to complement these ongoing efforts. In particular, hydrodynamic simulations must be vetted to ensure they are robust and sufficiently accurate over relevant characteristic scales. Verification models were generated in order to cultivate the technical knowledge and expertise needed to properly create, implement and execute numerical simulations. Furthermore, this effort was utilized extensively to educate students on the mathematical and numerical principles underlying hydrodynamic simulations. This education opportunity, provided in a holistic and rigorous manner, has greatly benefited developing scientists and engineers with the necessary understandings and toolsets required to excel at accomplishing the task at hand, and, more generally, it has enabled them to generate key programmatic deliverables. This report articulates several subtilties; specifically, how perturbations, nonlinear behavior, and dissipative mechanisms influence numerical stability, how to properly structure mathematical and numerical solutions, and how to properly generate error estimation/assignment. A more rigorous discussion of the consequences of such topics can be found in the body of this report in Chapters 2 and 3 with qualitative findings discussed in Chapter 4.

97 MATHEMATICS AND COMPUTING↗