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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds

A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.

Jardin, Matthew R.↗
NASA NTRS2014

Contributions of Astronauts Aerobic Exercise Intensity and Time on Change in VO2peak during Spaceflight

There is considerable variability among astronauts with respect to changes in maximal aerobic capacity (VO2peak) during International Space Station (ISS) missions, ranging from a 5% increase to 30% decline. Individual differences may be due to in-flight aerobic exercise time and intensity. PURPOSE: To evaluate the effects of in-flight aerobic exercise time and intensity on change in VO2peak during ISS missions. METHODS: Astronauts (N=11) performed peak cycle tests approx 60 days before flight (L-60), on flight day (FD) approx 14, and every approx 30 days thereafter. Metabolic gas analysis and heart rate (HR) were measured continuously during the test using the portable pulmonary function system. HR and duration of each in-flight cycle ergometer and treadmill (TM) session were recorded and averaged in time segments corresponding to each peak test. Mixed effects linear regression with exercise mode (TM or cycle) as a categorical variable was used to assess the contributions of exercise intensity (%time >70% peak HR or %time >90% peak HR) and time (min/wk), adjusted for body weight, on %change in VO2peak during the mission, and incorporating the repeated-measures experimental design. RESULTS: 110 observations were included in the model (4-6 peak cycle tests per astronaut, 2 exercise devices). VO2peak was reduced from preflight throughout the mission (FD14: 13+/-13% and FD 105: 8+/-10%). Exercise intensity (%peak HR: FD14=66+/-14; FD105=75+/-8) and time (min/wk: FD14=82+/-46; FD105=158+/-40) increased during flight. The models showed main effects for exercise time and intensity with no interactions between time, intensity, and device (70% peak HR: time [z-score=2.39; P=0.017], intensity [z-score=3.51; P=0.000]; 90% peak HR: time [zscore= 3.31; P=0.001], intensity [z-score=2.24; P=0.025]). CONCLUSION: Exercise time and intensity independently contribute to %change in VO2peak during ISS missions, indicating that there are minimal values for exercise time and intensity required to maintain VO2peak. As the FD105 average exercise intensity and time did not prevent a decline in VO2peak from preflight, astronauts' exercise prescriptions should target at least 160 min of weekly aerobic exercise at an average above 75% peak HR with increased time at intensities above 90% of peak HR starting early in the mission.

Downs, Meghan E.↗
NASA NTRSDate not supplied

Changes in Oculomotor Behavior and PVT Reaction Time During One Night of Sleep Deprivation

INTRODUCTION: The Psychomotor Vigilance Test (PVT) is a widely used objective measure of sustained attention, alertness, and fatigue. Previous studies consistently show that prolonged wakefulness and disrupted sleep patterns lead to increased lapses of attention and slower reaction times. These findings have critical implications for various professions, including healthcare, aviation, transportation safety, and spaceflight. In this study, we employed linear mixed models (LMM) to investigate hourly-measured 5-minute PVT reaction times during one night of total sleep deprivation. Our goal was to characterize the contribution of homeostatic sleep pressure (time awake) and circadian phase (salivary melatonin levels) on the dynamics of PVT reaction time. MATERIALS & METHODS: Data from twelve human participants were used in the analysis. Participants were healthy non-smokers, aged 18 and 40, with normal sleep habits defined as Pittsburg Sleep Quality Index scores < 5, and Morningness – Eveningness Questionnaire scores > 42 and < 58, respectively. Participants followed a constant-routine protocol and arrived at the NASA sleep laboratory approximately 1 to 2 hours after their habitual waking time. Tympanic temperature was measured every 30 min to provide a real-time estimate of circadian phase. Participants were required to stay awake throughout the laboratory experiment, which continued until their tympanic temperature had returned to baseline levels. This approach ensured that we could capture each participant's circadian trough and recovery, typically occurring between 24 and 26 hours after waking. The PVT and saliva melatonin were measured every hour, starting approximately from 3 hours after awakening. More information about the measurement protocol can be found in the publication by Stone et al. We used PVT reaction times between 100 and 10000 ms to calculate Reciprocal Reaction Times (RRTs). LMM models were employed to assess the contribution of time awake and saliva melatonin levels on changes in RRTs. Two models were created: the first model treated time awake as a fixed effect and the second model considered both the salivary melatonin level and time awake as fixed effects. Participants were included as a random effect in both models. We compared the models using an Analysis of Variance (ANOVA). The models were computed using the 'lmer' function from the 'lme4' package in R, and LMM p-values were determined using Satterthwaite's method. RESULTS: We found that time awake had a statistically significant effect on PVT RRTs during one night of sleep deprivation [χ2 = 2132.4, df = 1, p < 0.001]. In addition, the model including both saliva melatonin levels and time awake was statistically significantly better than one that uses just time awake [χ2 = 17.4, df = 1, p < 0.001]. DISCUSSION & CONCLUSION: As expected, these preliminary results suggest that the time awake and circadian phase each contribute to performance reductions as measured by the PVT. Future analyses will explore the contributions of other factors to the model.

sleep deprivation↗
DOE OSTI2022

Space-Time Block Preconditioning for Incompressible Flow

Parallel-in-time methods have become increasingly popular in the simulation of time-dependent numerical PDEs, allowing for the efficient use of additional message passing interface processes when spatial parallelism saturates. Most methods treat the solution and parallelism in space and time separately. In contrast, all-at-once methods solve the full space-time system directly, largely treating time as simply another spatial dimension. All-at-once methods offer a number of benefits over separate treatment of space and time, most notably significantly increased parallelism and faster time to solution (when applicable). However, the development of fast, scalable all-at-once methods has largely been limited to time-dependent (advection-)diffusion problems. This paper introduces the concept of space-time block preconditioning for the all-at-once solution of incompressible flow. By extending well-known concepts of spatial block preconditioning to the space-time setting, we develop a block preconditioner whose application requires the solution of a space-time (advection-)diffusion equation in the velocity block, coupled with a pressure Schur complement approximation consisting of independent spatial solves at each time-step, and a space-time matrix-vector multiplication. The new method is tested on four classical models in incompressible flow. Finally, the results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect scalability in nonlinear Picard iteration count when applied to a nonlinear Navier--Stokes problem, and minimal overhead in terms of number of preconditioner applications compared with sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Robust Carbon Dioxide Plume Imaging Using Joint Tomographic Inversion of Seismic Onset Time and Distributed Pressure and Temperature Measurements (Final Report)

We develop and demonstrate rapid and cost-effective methodologies for spatiotemporal tracking of CO2 plumes during geologic sequestration using joint inversion of seismic data and distributed pressure and temperature measurements. Key elements of our methodology are: (a) a computationally efficient approach to pressure and temperature propagation, (b) analysis of time lapse seismic data using a novel ‘seismic onset time’ approach to detect fluid front propagation, and (c) data assimilation and uncertainty assessment via joint inversion of pressure, temperature and time lapse seismic data, and (d) validating the numerical tomographic inversion using a CO2 injection demonstration projects, specifically data collected from the from the Petra Nova Parish Holdings CCUS project in the West Ranch Field, Texas and the Chester-16 reef CO2 injection site in Northern Michigan which is part of the DOE Midwestern Carbon Sequestration Project. The research team is led by Texas A&M University and includes Battelle as a subcontractor with support from Shell, Anadarko, Chevron and JX Nippon. A carbon dioxide (CO2) water-alternating-gas (WAG) pilot was conducted to gain insights into tertiary oil recovery potential via CO2 flood in the West Ranch Field as part of the Petra Nova project, the world’s largest post-combustion CO2 capture and utilization initiative. With a fluvial formation geology and large contrasts in permeability, this is a challenging and novel application of CO2 enhanced oil recovery (EOR). We build a predictive dynamic model of the subsurface that incorporates the multiphase and compositional data acquired during the pilot operation. The calibrated model is used for the carbon dioxide plume imaging. The study began with an initialization of the pilot sector model extracted from a calibrated full-field model. The pilot model calibration follows a two-step hierarchical workflow. First, we performed a large-scale update of the permeability distribution by integrating available bottomhole pressure and multiphase production data. In the second step, local permeability field is fine-tuned using a streamline-based method to match CO2 breakthrough times at the producers. The predictive capability of the calibrated model was verified through two blind validation tests: (1) the model showed good agreement with saturation logs acquired at two observation wells; and (2) the model reproduced the CO2 recovery as a fraction of the injected CO2. The use of seismic onset times has shown great promise for integrating near-continuous seismic surveys for updating geologic models. In this study, we analyze the impact of seismic survey frequency on the onset time approach aiming to extend the application of onset time to infrequent seismic surveys. In addition, we quantitatively examine the nonlinearity of the onset time method and compare it to the commonly used amplitude inversion method. We carry out a sensitivity analysis of seismic survey frequency based on the complete seismic survey data (over 175 surveys) of steam injection in a heavy oil reservoir (Peace River Unit) in Canada. Our results show that an adequate onset time map can be obtained from the infrequent seismic surveys by interpolation between seismic surveys as long as there is no change in the dominant underlying physics between the successive surveys. The study also shows that nonlinearity of the onset time method can be -smaller than that of the amplitude inversion method by several orders of magnitude. Application to the Brugge benchmark case shows that the onset time method obtains comparable permeability update as the traditional seismic amplitude inversion method with faster computation and improved convergence characteristics. We extend the streamline-based data integration approach to incorporate distributed temperature sensor (DTS) data using the concept of thermal tracer travel time. Then, a hierarchical workflow composed of evolutionary and streamline methods is employed to jointly history match the DTS and pressure data. Finally, CO2 saturation and streamline maps are used to visualize the CO2 plume movement during the sequestration process. The hierarchical workflow is applied to a carbon sequestration project in a carbonate reef reservoir within the Northern Niagaran Pinnacle Reef Trend in Michigan, USA. The monitoring data set consists of distributed temperature sensing (DTS) data acquired at the injection well and a monitoring well, flowing bottom-hole pressure data at the injection well, and time-lapse pressure measurements at several locations along the monitoring well. The history matching results indicate that the CO2 movement is mostly restricted to the intended zones of injection which is consistent with an independent warm-back analysis of the temperature data. In addition to employing simulation models and inverse methods for CO2 plume imaging, we also initialized a data-driven technology for detecting inter-well connectivity based on production and pressure data. Our machine-learning framework is built on the statistical recurrent unit (SRU) model and interprets well-based injection/production data into inter-well connectivity without relying on a geologic model. We test it on synthetic and field-scale CO2 EOR projects utilizing the water-alternating-gas (WAG) process. The validation of the proposed data-driven inter-well connectivity assessment is performed using synthetic data from simulation models where inter-well connectivity can be easily measured using the streamline-based flux allocation. The SRU model is shown to offer excellent prediction performance on the synthetic case. Despite significant measurement noise and frequent well shut-ins imposed in the field-scale case, the SRU model offers good prediction accuracy, the overall relative error of the phase production rates at most producers ranges from 10% to 30%. It is shown that the dominant connections identified by the data-driven method and streamline method are in close agreement. Texas A&M University, the lead organization in the project, was primarily responsible for the development of tomographic approaches for CO2 plume mapping in conjunction with distributed pressure, temperature and seismic onset time data. Battelle, as a subcontractor, was primarily responsible for the development of analytical and empirical methods for analyzing transient injection rate and pressure data from point/line sources such as injection and monitoring wells. An additional area of emphasis for Battelle was the use of machine learning for such tasks as inferring reservoir connectivity information from injection-production data, and identifying variable importance for machine learning-based proxy models developed from full-physics simulations. The two organizations also collaborated on the application of the tomographic inversion methodology for a field data set.

02 PETROLEUM↗
DOE OSTI2023

Inferring Viral Transmission Time from Phylogenies for Known Transmission Pairs

When the time of an HIV transmission event is unknown, methods to identify it from virus genetic data can reveal the circumstances that enable transmission. We developed a single-parameter Markov model to infer transmission time from an HIV phylogeny constructed of multiple virus sequences from people in a transmission pair. Our method finds the statistical support for transmission occurring in different possible time slices. We compared our time-slice model results to previously described methods: a tree-based logical transmission interval, a simple parsimony-like rules-based method, and a more complex coalescent model. Across simulations with multiple transmitted lineages, different transmission times relative to the source’s infection, and different sampling times relative to transmission, we found that overall our time-slice model provided accurate and narrower estimates of the time of transmission. We also identified situations when transmission time or direction was difficult to estimate by any method, particularly when transmission occurred long after the source was infected and when sampling occurred long after transmission. Applying our model to real HIV transmission pairs showed some agreement with facts known from the case investigations. We also found, however, that uncertainty on the inferred transmission time was driven more by uncertainty from time calibration of the phylogeny than from the model inference itself. Encouragingly, comparable performance of the Markov time-slice model and the coalescent model—which make use of different information within a tree—suggests that a new method remains to be described that will make full use of the topology and node times for improved transmission time inference.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Genetic variation associated with adult migration timing in lineages of Steelhead and Chinook Salmon in the Columbia River

Abstract With the discovery of a major effect region (GREB1L, ROCK1) for adult migration timing in genomes of both Chinook Salmon and Steelhead, several subsequent studies have investigated the effect size and distribution of early and late migration alleles among populations in the Columbia River. Here, we synthesize the results of these studies for the major lineages of Chinook Salmon and Steelhead that include highly distinct groups in the interior Columbia River that exhibit atypical life histories from most coastal lineage populations of these two species. Whole‐genome studies with high marker density have provided extensive insight into SNPs most associated with adult migration timing, and suites of markers for each species have been genotyped in large numbers of individuals to further validate phenotypic effects. For Steelhead, the largest phenotypic effect sizes have been observed in the coastal lineage (36% of variation for passage timing at Bonneville Dam; 43% of variation for tributary arrival timing) compared to the inland lineage (7.5% of variation for passage timing at Bonneville Dam; 8.4% of variation for tributary arrival timing) that overwinter in freshwater prior to spawning. For Chinook Salmon, large effect sizes have been observed in all three lineages for multiple adult migration phenotypes (Coastal lineage: percentage of variation of 27.9% for passage timing at Bonneville Dam, 28.7% for arrival timing for spawning; Interior ocean type: percentage of variation of 47.6% for passage timing at Bonneville Dam, 39.6% for tributary arrival timing, 77.9% for arrival timing for spawning; Interior stream type: percentage of variation of 35.3% for passage at Bonneville Dam, 9.8% for tributary arrival timing, 4.7% for arrival timing for spawning). Together, these results have extended our understanding of genetic variation associated with life history diversity in distinct populations of the Columbia River, however, much research remains necessary to determine the causal mechanism for this major effect region on migration timing in these species.

Narum, Shawn R.↗
DOE OSTI2025

Estimating time in quantum chaotic systems and black holes

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation". Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity.

Black holes↗
NASA NTRS2000

Team Training and Retention of Skills Acquired Above Real Time Training on a Flight Simulator

Above Real-Time Training (ARTT) is the training acquired on a real time simulator when it is modified to present events at a faster pace than normal. The experiments related to training of pilots performed by NASA engineers (Kolf in 1973, Hoey in 1976) and others (Guckenberger, Crane and their associates in the nineties) have shown that in comparison with the real time training (RTT), ARTT provides the following benefits: increased rate of skill acquisition, reduced simulator and aircraft training time, and more effective training for emergency procedures. Two sets of experiments have been performed; they are reported in professional conferences and the respective papers are included in this report. The retention of effects of ARTT has been studied in the first set of experiments and the use of ARTT as top-off training has been examined in the second set of experiments. In ARTT, the pace of events was 1.5 times the pace in RTT. In both sets of experiments, university students were trained to perform an aerial gunnery task. The training unit was equipped with a joystick and a throttle. The student acted as a nose gunner in a hypothetical two place attack aircraft. The flight simulation software was installed on a Universal Distributed Interactive Simulator platform supplied by ECC International of Orlando, Florida. In the first set of experiments, two training programs RTT or ART7 were used. Students were then tested in real time on more demanding scenarios: either immediately after training or two days later. The effects of ARTT did not decrease over a two day retention interval and ARTT was more time efficient than real time training. Therefore, equal test performance could be achieved with less clock-time spent in the simulator. In the second set of experiments three training programs RTT or ARTT or RARTT, were used. In RTT, students received 36 minutes of real time training. In ARTT, students received 36 minutes of above real time training. In RARTT, students received 18 minutes of real time training and 18 minutes of above real time training as top-off training. Students were then tested in real time on more demanding scenarios. The use of ARTT as top-off training after RTT offered better training than RTT alone or ARTT alone. It is, however, suggested that a similar experiment be conducted on a relatively more complex task with a larger sample of participants. Within the proposed duration of the research effort, the setting up of experiments and trial runs on using ARTT for team training were also scheduled but they could not be accomplished due to extra ordinary challenges faced in developing the required software configuration. Team training is, however, scheduled in a future study sponsored by NASA at Tuskegee University.

Ali, Syed Friasat↗
DOE OSTI2024

Full time-dependent SOLPS-ITER simulation of the SPARC tokamak: actuator design for particle and divertor condition control *

Abstract This paper presents the application of full time-dependent SOLPS-ITER simulations for actuator design in the SPARC tokamak. This study employs both the EIRENE module, a neutral solver, and the B2.5 plasma module in a time-dependent mode. This is in contrast to most SOLPS simulations, which focus on steady-state solutions, where the neutral distribution is evolved without any time limit or for a time step of 1 ⋅ 10 − 3 second, which is several orders of magnitude larger than the fluid plasma time step. The time-dependent EIRENE was tested with a fixed B2.5 background and compared with a simple conductance based model in a simplified pump chamber geometry. This comparison aimed to verify the reliability of the neutral relaxation timescale derived from the time-dependent EIRENE. Subsequently, a full time-dependent simulation was performed in a realistic geometry, with the Monte-Carlo neutral time step synchronized with the plasma fluid time step. The numerical setup of the code, including relative time steps and the size of the census data used to store Monte-Carlo particle information is considered. The full-time dependent simulations are then applied to inform the design of the SPARC louver structure, which affects divertor plasma parameters by regulating the neutral conductance from the divertor to the pump. The response of the plasma and neutral parameters was captured on a timescale that enables the design of the actuator to consider time-dependent control capability. It was found that changing the louver opacity has an equivalent effect as varying the gas throughput via puff actuation. Therefore, equivalent divertor plasma conditions can be obtained from both actuators, while the neutral pressure distribution in the pump and divertor differs for each actuator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2005

VERSE - Virtual Equivalent Real-time Simulation

Distributed real-time simulations provide important timing validation and hardware in the- loop results for the spacecraft flight software development cycle. Occasionally, the need for higher fidelity modeling and more comprehensive debugging capabilities - combined with a limited amount of computational resources - calls for a non real-time simulation environment that mimics the real-time environment. By creating a non real-time environment that accommodates simulations and flight software designed for a multi-CPU real-time system, we can save development time, cut mission costs, and reduce the likelihood of errors. This paper presents such a solution: Virtual Equivalent Real-time Simulation Environment (VERSE). VERSE turns the real-time operating system RTAI (Real-time Application Interface) into an event driven simulator that runs in virtual real time. Designed to keep the original RTAI architecture as intact as possible, and therefore inheriting RTAI's many capabilities, VERSE was implemented with remarkably little change to the RTAI source code. This small footprint together with use of the same API allows users to easily run the same application in both real-time and virtual time environments. VERSE has been used to build a workstation testbed for NASA's Space Interferometry Mission (SIM PlanetQuest) instrument flight software. With its flexible simulation controls and inexpensive setup and replication costs, VERSE will become an invaluable tool in future mission development.

virtual real time↗
DOE OSTI2020

Parallel-in-Time Multigrid Methods for Hyperbolic Problems, with a Focus on the Shallow Water Equations

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations, which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic problems of programmatic interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic problems on future architectures. The difficulty lies in the fact that hyperbolic problems are well-known to be difficult for parallel-in-time methods, with the most common parallel-in-time method, Parareal, diverging in many cases. Here, the chosen methodology for scalably solving these hyperbolic space-time equations is multigrid-reductionin-time (MGRIT), because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. To further research in this area, this project will explore a model hyperbolic problem (the shallow water equations) in the context of recent advances (e.g., by Wingate and Haut) in constructing improved coarse time-grid time-propagators by using the slow asymptotic structure of the equations. In particular, we will investigate if such coarse time-propagators offer significant advantages in an MGRIT setting, and explore any broader insights gained into parallel-in-time for hyperbolic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallelin-time methods, with the most common method, parareal, diverging in many cases. The current state-of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be implemented in a high-performance but general way in XBraid and explored for more complicated problems. We will additionally research, as time allows, improvements to these techniques, as well as multigrid relaxation techniques based on Least Squares Shadowing (LSS by Wang) and a nonintrusive block tridiagonal solver based on MGRIT, called TriMGRIT.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Simplified Two-Time Step Method for Calculating Combustion and Emission Rates of Jet-A and Methane Fuel With and Without Water Injection

A simplified kinetic scheme for Jet-A, and methane fuels with water injection was developed to be used in numerical combustion codes, such as the National Combustor Code (NCC) or even simple FORTRAN codes. The two time step method is either an initial time averaged value (step one) or an instantaneous value (step two). The switch is based on the water concentration in moles/cc of 1x10(exp -20). The results presented here results in a correlation that gives the chemical kinetic time as two separate functions. This two time step method is used as opposed to a one step time averaged method previously developed to determine the chemical kinetic time with increased accuracy. The first time averaged step is used at the initial times for smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, initial water to fuel mass ratio, temperature, and pressure. The second instantaneous step, to be used with higher water concentrations, gives the chemical kinetic time as a function of instantaneous fuel and water mole concentration, pressure and temperature (T4). The simple correlations would then be compared to the turbulent mixing times to determine the limiting rates of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. Chemical kinetic time equations for fuel, carbon monoxide and NOx are obtained for Jet-A fuel and methane with and without water injection to water mass loadings of 2/1 water to fuel. A similar correlation was also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium concentrations of carbon monoxide and nitrogen oxide as functions of overall equivalence ratio, water to fuel mass ratio, pressure and temperature (T3). The temperature of the gas entering the turbine (T4) was also correlated as a function of the initial combustor temperature (T3), equivalence ratio, water to fuel mass ratio, and pressure.

Molnar, Melissa↗
NASA NTRS2011

Time Synchronization and Distribution Mechanisms for Space Networks

This work discusses research on the problems of synchronizing and distributing time information between spacecraft based on the Network Time Protocol (NTP), where NTP is a standard time synchronization protocol widely used in the terrestrial network. The Proximity-1 Space Link Interleaved Time Synchronization (PITS) Protocol was designed and developed for synchronizing spacecraft that are in proximity where proximity is less than 100,000 km distant. A particular application is synchronization between a Mars orbiter and rover. Lunar scenarios as well as outer-planet deep space mother-ship-probe missions may also apply. Spacecraft with more accurate time information functions as a time-server, and the other spacecraft functions as a time-client. PITS can be easily integrated and adaptable to the CCSDS Proximity-1 Space Link Protocol with minor modifications. In particular, PITS can take advantage of the timestamping strategy that underlying link layer functionality provides for accurate time offset calculation. The PITS algorithm achieves time synchronization with eight consecutive space network time packet exchanges between two spacecraft. PITS can detect and avoid possible errors from receiving duplicate and out-of-order packets by comparing with the current state variables and timestamps. Further, PITS is able to detect error events and autonomously recover from unexpected events that can possibly occur during the time synchronization and distribution process. This capability achieves an additional level of protocol protection on top of CRC or Error Correction Codes. PITS is a lightweight and efficient protocol, eliminating the needs for explicit frame sequence number and long buffer storage. The PITS protocol is capable of providing time synchronization and distribution services for a more general domain where multiple entities need to achieve time synchronization using a single point-to-point link.

Woo, Simon S.↗
NASA NTRS2013

Electro-Optic Time-to-Space Converter for Optical Detector Jitter Mitigation

A common problem in optical detection is determining the arrival time of a weak optical pulse that may comprise only one to a few photons. Currently, this problem is solved by using a photodetector to convert the optical signal to an electronic signal. The timing of the electrical signal is used to infer the timing of the optical pulse, but error is introduced by random delay between the absorption of the optical pulse and the creation of the electrical one. To eliminate this error, a time-to-space converter separates a sequence of optical pulses and sends them to different photodetectors, depending on their arrival time. The random delay, called jitter, is at least 20 picoseconds for the best detectors capable of detecting the weakest optical pulses, a single photon, and can be as great as 500 picoseconds. This limits the resolution with which the timing of the optical pulse can be measured. The time-to-space converter overcomes this limitation. Generally, the time-to-space converter imparts a time-dependent momentum shift to the incoming optical pulses, followed by an optical system that separates photons of different momenta. As an example, an electro-optic phase modulator can be used to apply longitudinal momentum changes (frequency changes) that vary in time, followed by an optical spectrometer (such as a diffraction grating), which separates photons with different momenta into different paths and directs them to impinge upon an array of photodetectors. The pulse arrival time is then inferred by measuring which photodetector receives the pulse. The use of a time-to-space converter mitigates detector jitter and improves the resolution with which the timing of an optical pulse is determined. Also, the application of the converter enables the demodulation of a pulse position modulated signal (PPM) at higher bandwidths than using previous photodetector technology. This allows the creation of a receiver for a communication system with high bandwidth and high bits/photon efficiency.

Birnbaum, Kevin↗
NASA NTRS2022

A Waveform Skewness Index for Measuring Time Series Nonlinearity and Its Applications to the ENSO-Indian Monsoon Relationship

Many geophysical time series possess nonlinear characteristics that reflect the underlying physics of the phenomena the time series describe. The nonlinear character of times series can change with time, so it is important to quantify time series nonlinearity without assuming stationarity. A common way of quantifying the time evolution of time series nonlinearity is to compute sliding skewness time series, but it is shown here that such an approach can be misleading when time series contain periodicities. To remedy this deficiency of skewness, a new waveform skewness index is proposed for quantifying local nonlinearities embedded in time series. A waveform skewness spectrum is proposed for determining the frequency components that are contributing to time series waveform skewness. The new methods are applied to the El Niño–Southern Oscillation (ENSO) and the Indian monsoon to test a recently proposed hypothesis that states that changes in the ENSO–Indian monsoon relationship are related to ENSO nonlinearity. We show that the ENSO–Indian rainfall relationship weakens during time periods of high ENSO waveform skewness. The results from two different analyses suggest that the breakdown of the ENSO–Indian monsoon relationship during time periods of high ENSO waveform skewness is related to the more frequent occurrence of strong central Pacific El Niño events, supporting arguments that changes in the ENSO–Indian rainfall relationship are not solely related to noise.

Justin Schulte↗
DOE OSTI2020

A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics

This work describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (Parallel time integration with multigrid. https://computation.llnl.gov/projects/parallel-timeintegration-multigrid) and Chombo (Chombo software package for AMR applications—design document, 2014). The former is a parallel time integration library using multigrid and the latter is a massively parallel structured AMR library. Employing this adaptive space-time parallel algorithm is Chord (Comput Fluids 123:202–217, 2015), a computational fluid dynamics (CFD) application code for solving compressible fluid dynamics problems. For the same solution accuracy, speedups are demonstrated from the use of space-time parallelization over the time-sequential integration on Couette flow and Stokes’ second problem. On a transient Couette flow case, at least a 1.5× speedup is achieved, and with a time periodic problem, a speedup of up to 13.7× over the time-sequential case is obtained. In both cases, the speedup is achieved by adding processors and exploring additional parallelization in time. The numerical experiments show the algorithm is promising for CFD applications that can take advantage of the time parallelism. Future work will focus on improving the parallel performance and providing more tests with complex fluid dynamics to demonstrate the full potential of the algorithm.

97 MATHEMATICS AND COMPUTING↗