On the stability of numerical solutions of ordinary differential equations
Relative and absolute stability regions determined for numerical solutions of ordinary differential equations
STABILITY↗
SEARCH · Engineering Papers
Results for “numerical relativity”
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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Numerical Arc Segmentation Algorithm for a Radio Conference-NASARC (version 4.0) technical manual
The information contained in the NASARC (Version 4.0) Technical Manual and NASARC (Version 4.0) User's Manual relates to the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through November 1, 1988. The Technical Manual describes the NASARC concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions were incorporated in the Version 4.0 software over prior versions. These revisions have further enhanced the modeling capabilities of the NASARC procedure and provide improved arrangements of predetermined arcs within the geostationary orbits. Array dimensions within the software were structured to fit within the currently available 12 megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 4.0) allows worldwide planning problem scenarios to be accommodated within computer run time and memory constraints with enhanced likelihood and ease of solution.
Whyte, Wayne A., Jr.↗
Relativistic gas accretion onto supermassive black hole binaries from inspiral through merger
Accreting supermassive black hole binaries are powerful multimessenger sources emitting both gravitational and electromagnetic (EM) radiation. Understanding the accretion dynamics of these systems and predicting their distinctive EM signals is crucial to informing and guiding upcoming efforts aimed at detecting gravitational waves produced by these binaries. To this end, accurate numerical modeling is required to describe both the spacetime and the magnetized gas around the black holes. In this paper, we present two key advances in this field of research. First, we have developed a novel 3D general relativistic magnetohydrodynamics (GRMHD) framework that combines multiple numerical codes to simulate the inspiral and merger of supermassive black hole binaries starting from realistic initial data and running all the way through merger. Throughout the evolution, we adopt a simple but functional prescription to account for gas cooling through photon emission. Next, we have applied our new computational method to follow the time evolution of a circular, equal-mass, nonspinning black hole binary for ∼200 orbits, starting from a separation of 20𝑟 𝑔 and reaching the postmerger evolutionary stage of the system. We have shown how mass continues to flow toward the binary even after the binary “decouples” from its surrounding disk, but the accretion rate onto the black holes diminishes. We have identified how the minidisks orbiting each black hole are slowly drained and eventually dissolve as the binary compresses. We confirm previous findings that the system’s luminosity decreases by a factor of a few during inspiral; however, we observe an abrupt increase by ∼50% in this quantity at the time of merger, likely accompanied by an equally abrupt change in spectrum. Lastly, we have demonstrated that during the inspiral, fluid ram pressure regulates the fraction of the magnetic flux transported to the binary that attaches to the black holes’ horizons.
Accretion disk & black-hole plasma↗
The ion-ion acoustic instability
This paper considers the linear theory of ion-acoustic-like instabilities in a homogeneous Vlasov plasma with two ion components, a less dense beam and a more dense core, with a relative drift velocity. Numerical solutions of the full electrostatic dispersion equation are presented, and the properties of the ion-ion acoustic instability are studied in detail. At relatively cold beam temperatures, the instability is fluid-like, but it becomes a beam resonant kinetic instability as the beam temperature becomes of the order of the core temperature; if the mode is unstable, its threshold lies well below the threshold of the electron-ion acoustic instability. An electron temperature anisotropy enhances the instability, and at sufficiently large beam-core relative drift speeds, electron magnetization can either detract from or enhance the instability.
Gary, S. Peter↗
Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Long-term uncertainty quantification in WRF-modeled offshore wind resource off the US Atlantic coast
Uncertainty quantification of long-term modeled wind speed is essential to ensure stakeholders can best leverage wind resource numerical data sets. Offshore, this need is even stronger given the limited availability of observations of wind speed at heights relevant for wind energy purposes and the resulting heavier relative weight of numerical data sets for wind energy planning and operational projects. In this analysis, we consider the National Renewable Energy Laboratory's 21-year updated numerical offshore data set for the US East Coast and provide a methodological framework to leverage both floating lidar and near-surface buoy observations in the region to quantify uncertainty in the modeled hub-height wind resource. We first show how using a numerical ensemble to quantify the uncertainty in modeled wind speed is insufficient to fully capture the model deviation from real-world observations. Next, we train and validate a random forest to vertically extrapolate near-surface wind speed to hub height using the available short-term lidar data sets in the region. We then apply this model to vertically extrapolate the long-term near-surface buoy wind speed observations to hub height so that they can be directly compared to the long-term numerical data set. We find that the mean 21-year uncertainty in 140 m hourly average wind speed is slightly lower than 3 m s -1 (roughly 30m% of the mean observed wind speed) across the considered region. Atmospheric stability is strictly connected to the modeled wind speed uncertainty, with stable conditions associated with an uncertainty which is, on average, about 20 % larger than the overall mean uncertainty.
17 WIND ENERGY↗
A linear MHD instability analysis of solar mass ejections with gravitation
The linear MHD instability of a cylindrical plasma is used to investigate the origin of solar mass ejections, and the dispersion relation is solved numerically. The initial plasma-flow velocity is found to have a significant effect on the instability criteria and growth rate, and the instability growth-rate is shown to be larger in cases where plasma flow exists, relative to the static case. Results suggest that the plasma column may break into small pieces. Assuming a thin-tube approximation, gravity is found to have little effect on the instability of quasi-horizontal ejection, but to have considerable effect on the vertical ejection. In considering the gravitational force, an exact analytical solution is found for the vertical case, while asymptotic solutions are given for the horizontal and oblique cases.
Song, M. T.↗
Comment on 'Shang S. 2012. Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes 26: 3338-3343. DOI: 10.1002/hyp.8405'
A previous study analyzed errors in the numerical calculation of actual crop evapotranspiration (ET(sub a)) under soil water stress. Assuming no irrigation or precipitation, it constructed equations for ET(sub a) over limited soil-water ranges in a root zone drying out due to evapotranspiration. It then used a single crop-soil composite to provide recommendations about the appropriate usage of numerical methods under different values of the time step and the maximum crop evapotranspiration (ET(sub c)). This comment reformulates those ET(sub a) equations for applicability over the full range of soil water values, revealing a dependence of the relative error in numerical ET(sub a) on the initial soil water that was not seen in the previous study. It is shown that the recommendations based on a single crop-soil composite can be invalid for other crop-soil composites. Finally, a consideration of the numerical error in the time-cumulative value of ET(sub a) is discussed besides the existing consideration of that error over individual time steps as done in the previous study. This cumulative ET(sub a) is more relevant to the final crop yield.
Time step↗
Analysis and modeling of summertime convective cloud and precipitation structure over the southeastern United States
Described is work performed under NASA Grant NAG8-654 for the period 15 March to 15 September 1988. This work entails primarily data analysis and numerical modeling efforts related to the 1986 Satellite Precipitation and Cloud Experiment (SPACE). In the following, the SPACE acronym is used along with the acronym COHMEX, which represents the encompassing Cooperative Huntsville Meteorological Experiment. Progress made during the second half of the first year of the study included: (1) installation and testing of the RAMS numerical Modeling system on the Alabama CRAY X-MP/24; (2) a start on the analysis of the mesoscale convection system (MCS) of 13 July 1986 COHMEX case; and (3) a cursory examination of a small MCS that formed over the COHMEX region on 15 July 1986. Details of each of these individual tasks are given.
Knupp, Kevin R.↗
Investigating the Molecular Response in Irradiated Yeast in Support of the BioSentinel CubeSat Mission
The BioSentinel CubeSat mission is NASA’s first deep space bioscience mission scheduled to fly as a secondary payload onboard Artemis I. BioSentinel seeks to understand the impacts of deep space radiation on living organisms using the model organism Saccharomyces cerevisiae, or budding yeast. In recent years, the BioSentinel team has conducted ground-based investigations into the effects of ionizing radiation (IR) on budding yeast to better understand spaceflight data. One investigation focuses on the impacts of radiation on budding yeast metabolics using the redox dye alamarBlue, an indicator that will also be used onboard BioSentinel. In this investigation, we have observed metabolic changes in both wild-type and in mutant yeast cells deficient in DNA repair. The focus of our research is to support the ongoing investigation into the molecular mechanisms that explain these observed changes. To do this, we first conducted preliminary research into the metabolic processes of S. cerevisiae to identify any potential vulnerabilities to radiation. We then conducted a statistical kinetic analysis on past experimental metabolic data, in addition to an analysis of data from a multisensor metabolic rig experiment. Ultimately, we identified numerous redox-related changes with increasing doses of radiation in both wild-type and mutant cells. These findings highlight the mitochondrial Electron Transport Chain (ETC) as a potential candidate process to account for these observed changes. Specifically, we are focused on the electron carriers of the ETC, including NADH and FADH2, given their participation in numerous redox mechanisms. We propose future experiments, including NADH assays, an investigation into the glycerol-3-phosphate shuttle, and investigations into other ETC complexes.
BioSentinel↗
A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media
This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Uncertainties in Simulating Flooding During Hurricane Harvey Using 2D Shallow Water Equations
Abstract Flooding is one of the most impactful weather‐related natural hazards. Numerical models that solve the two dimensional (2D) shallow water equations (SWE) represent the first‐principles approach to simulate all types of spatial flooding, such as pluvial, fluvial, and coastal flooding, and their compound dynamics. High spatial resolution (e.g., () m) is needed in 2D SWE simulations to capture flood dynamics accurately, resulting in formidable computational challenges. Thus, relatively coarser spatial resolutions are used for large‐scale simulations of flooding, which introduce uncertainties in the results. It is unclear how the uncertainty associated with the model resolution compares to the uncertainties in precipitation data sets and assumptions regarding boundary conditions when channelized flows interact with other water bodies. In this study, we compare these three sources of uncertainties in 2D SWE simulations for the 2017 Houston flooding event. Our results show that precipitation uncertainty and mesh resolution have more significant impacts on the simulated streamflow and inundation dynamics than the choice of the downstream boundary condition at the watershed outlet. We point out the viability to confine the uncertainty of coarsening mesh resolution by using the variable resolution mesh (VRM) which refines critical topographic features with far fewer grid cells. Specifically, in simulations with VRM, the simulated inundation depths over the refined region are comparable to that use the finest uniform mesh. This study contributes to understanding the challenges and pathways for applying 2D SWE models to improve the realism of flood simulations over large scales.
54 ENVIRONMENTAL SCIENCES↗
Numerical and experimental analysis of a thin liquid film on a rotating disk related to development of a spacecraft absorption cooling system
The numerical and experimental analysis of a thin liquid film on a rotating and a stationary disk related to the development of an absorber unit for a high capacity spacecraft absorption cooling system, is described. The creation of artificial gravity by the use of a centrifugal field was focused upon in this report. Areas covered include: (1) One-dimensional computation of thin liquid film flows; (2) Experimental measurement of film height and visualization of flow; (3) Two-dimensional computation of the free surface flow of a thin liquid film using a pressure optimization method; (4) Computation of heat transfer in two-dimensional thin film flow; (5) Development of a new computational methodology for the free surface flows using a permeable wall; (6) Analysis of fluid flow and heat transfer in a thin film in the presence and absence of gravity; and (7) Comparison of theoretical prediction and experimental data. The basic phenomena related to fluid flow and heat transfer on rotating systems reported here can also be applied to other areas of space systems.
Faghri, Amir↗
On direct numerical simulations of turbulent reacting flows
A description of the emerging field of direct numerical simulations of turbulent, chemically reacting flows is presented. The types of direct numerical simulations, physical issues related to implementing the simulations, as well as the various numerical methods used are described. Examples are presented of recent applications of direct numerical simulations to a variety of problems, displaying both the potential of the method and also some of its limitations. Finally, our view of the potential role of direct numerical simulations in future research on turbulent, chemically reacting flows is presented.
Jou, W.-H.↗
A Numerical Method for Calculating the Wave Drag of a Configuration from the Second Derivative of the Area Distribution of a Series of Equivalent Bodies of Revolution
A method based on linearized and slender-body theories, which is easily adapted to electronic-machine computing equipment, is developed for calculating the zero-lift wave drag of single- and multiple-component configurations from a knowledge of the second derivative of the area distribution of a series of equivalent bodies of revolution. The accuracy and computational time required of the method to calculate zero-lift wave drag is evaluated relative to another numerical method which employs the Tchebichef form of harmonic analysis of the area distribution of a series of equivalent bodies of revolution. The results of the evaluation indicate that the total zero-lift wave drag of a multiple-component configuration can generally be calculated most accurately as the sum of the zero-lift wave drag of each component alone plus the zero-lift interference wave drag between all pairs of components. The accuracy and computational time required of both methods to calculate total zero-lift wave drag at supersonic Mach numbers is comparable for airplane-type configurations. For systems of bodies of revolution both methods yield similar results with comparable accuracy; however, the present method only requires up to 60 percent of the computing time required of the harmonic-analysis method for two bodies of revolution and less time for a larger number of bodies.
Levy, Lionel L., Jr.↗
Numerical simulation: Its contributions to turbulence modeling
The relative advantages and disadvantages of Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are discussed. The topics are presented in viewgraph form.
Ferziger, Joel H.↗
A Detailed Vehicle Simulation Process to Support CAFE and CO 2 Standards (MY 2021–2026 Final Rule Analysis)
In 1975, Congress passed the Energy Policy and Conservation Act (EPCA), requiring standards for corporate average fuel economy (CAFE), and charging the U.S. Department of Transportation (DOT) with the establishment and enforcement of these standards. The Secretary of Transportation has delegated these responsibilities to the National Highway Traffic Safety Administration (NHTSA). NHTSA has contracted the DOT Volpe National Transportation Systems Center (Volpe Center) to provide analytical support for NHTSA’s regulatory and analytical activities related to fuel economy standards. Unlike long-standing safety and criteria pollutant emissions standards, fuel economy standards apply to manufacturers’ overall fleets rather than to individual vehicle models. In developing the standards, NHTSA made use of the CAFE Compliance and Effects Modeling System (the “CAFE model”), which was developed by DOT’s Volpe Center for the 2005-2007 CAFE rulemaking and has been continually updated since. The model is the primary tool used by the agency to evaluate potential CAFE stringency levels by applying technologies incrementally to each manufacturer’s fleet until the requirements under consideration are met. The CAFE model relies on numerous technology-related and economic inputs such as market forecasts and technology cost and effectiveness estimates; these inputs are categorized by vehicle classification, technology synergies, phase-in rates, cost learning curve adjustments, and technology “decision trees.” The Volpe Center assists NHTSA in the development of the engineering and economic inputs to the CAFE model by analyzing the application of potential technologies to the current automotive industry vehicle fleet to determine the feasibility of future CAFE standards, the associated costs, and the benefits of the standards.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Some notes on the numerical solution of shear-lag and mathematically related problems
The analysis of box beams with shear deformation of the flanges can be reduced to the solution of a differential equation. The same equation is met in other problems of stress analysis. No analytical solutions of this equation can be given for practical cases, and numerical methods of evaluation must be used. Available methods are briefly discussed. Two numerical examples show the application of the step-by-step method of integration to shear-lag problems.
Kuhn, Paul↗