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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 OSTI2015

Water Start Up Time Model Validation Test

This report is an Oregon Institute of Technology thesis project completed in partial fulfillment for the Masters of Science in Renewable Energy Engineering degree. The testing and research done for this report, investigate the phenomena of water start up time in the spiral case of hydro units. Water start up time is defined as the time it takes for water to accelerate from zero to rated velocity. From analysis of the literature there shows no published article of water start up time being measured and compared to theoretically calculated values. However a multiplier is used to create a buffer in the estimations of water start up time to use in the engineering and selection of governors for hydro units. The multiplier has also been widely used in computer model simulations which causes a dependence of this multiplier. In 2013 an article was published which challenges the hypothesis that water start up time has been over hypothesized and that the multiplier would be of a smaller value than what was hypothesized which would mean that the governing ability is more than what was expected. This proposal of a higher governing ability would mean that the hydro facilities that are currently standing has a higher stability rating than what was initially thought. The higher stability would allow for increased penetration of renewables onto the electrical grid. The lack of actual water start up time measurements as well as the infeasibility of testing on an actual hydro unit meant that a model would need to be designed, built, and tested. The model had two testing parameters that were examined. One of the parameters was flow rate that was controlled by the number of wicket gates that was installed into the system and the other was the reference height from the forebay to tail water. There were one hundred results from the test trials. The data from the trials showed a trend for the multiplier which was not constant as previously hypothesized and instead illustrated a parabolic trend that tapers into a linear digression. This result means that the range of testing was insufficient and the height range in which the trials were taking placed was subjected to higher variability. The results showed that the multiplier used in water start up time is not a constant and is variable based on the water level. The previous hypothesis stating that the water start up time is faster is false. In accordance with the results the trend showed that the actual water start up time is slower than what is hypothesized. This means at lower water levels the hypothesized governing ability is actually less than what is calculated to be using the current method of water start up time calculation for spiral cases. The theoretical analysis showed that with increased water level and flow rate showed that the multiplier has less effect on water start up time. The value of the water start up time tapering off from the experimental data shows that the trend for water start up time for both theoretical and experimental share similarities. An increased testing range of the water level in the trials will hypothetically lower the variability of the multiplier and in turn conform to a linear equation. The linear equation is shown to approach zero with increased head in which a static value can be achieved for a specified range.

13 HYDRO ENERGY↗

DOE OSTI2016

Impacts of Recycling Time on Fuel Cycle Transition

The purpose of this work is to show the importance of assumptions regarding the recycling time for time-dependent fuel cycle scenarios that involve transition from the current state of the U.S. fuel cycle to cycles based on continuous recycling via fast reactors. The recycling time is defined here as the total time between when the fuel is discharged from the reactor core and when its recovered heavy metals (HM) are recycled back into the core as part of the fresh/new fuel. The main processes occurring within the recycling time include cooling, separations, and fuel fabrication. The minimum recycling time required for fast reactor fuel largely depends on the minimum cooling time, which will be longer if discharged fuel needs to be moved to a centrally-located separations facility. A longer cooling time is needed for the heat load and fuel characteristics to reach safer levels for handling and transportation. Therefore, if the separation and fabrication facilities were co-located with reactors on-site, then the total recycling time could be reduced by several years. For fuel cycle transition scenarios in which external fissile materials (Pu or TRU) are limiting, these longer recycling times may prolong the transition to the continuous recycling system of fast reactors as well as impact the fuel cycle system performance during the transition. Therefore, in order to demonstrate the quantitative impacts of these recycling time assumptions, an example scenario of transition to the fast reactor fleet with continuous recycle was modeled in the fuel cycle systems code DYMOND. It must be emphasized that this is a point study that demonstrates how a longer recycling time can impact the rate of transition under specific conditions and assumptions. For alternative scenarios, such as those in which there are no fissile material constraints, there are likely no significant impacts due to recycling time. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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 OSTI2013

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: Accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for “flip-flop” conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

SU-G-JeP3-07: Real-Time Image Guided Radiation Therapy for Heterotopic Ossification in Patients After Hip Replacement

Purpose: To demonstrate the feasibility of using CBCT in a real-time image guided radiation therapy (IGRT) for single fraction heterotopic ossification (HO) in patients after hip replacement. In this real-time procedure, all steps, from simulation, imaging, planning to treatment delivery, are performed at the treatment unit in one appointment time slot. This work promotes real-time treatment to create a paradigm shift in the single fraction radiation therapy. Methods: An integrated real-time IGRT for HO was developed and tested for radiation treatment of heterotopic ossification for patient after hip replacement. After CBCT images are acquired at the linac, and sent to the treatment planning system, the physician determines the field and/or draws a block. Subsequently, a simple 2D AP/PA plan with prescription of 700 cGy is created on-the-fly for physician to review. Once the physician approves the plan, the patient is treated on the same simulation position. This real-time treatment requires the team of attending physician, physicist, therapists, and dosimetrist to work in harmony to achieve all the steps in a timely manner. Results: Ten patients have been treated with this real-time treatment, having the same beams arrangement treatment plan and prescription as our clinically regular CT-based 2D plans. The average time for these procedures are 52.9 ±10.7 minutes from the time patient entered the treatment room until s/he exited, and 37.7 ±8.6 minutes from starting CBCT until last beam delivered. Conclusion: The real-time IGRT for HO treatment has been tested and implemented to be a clinically accepted procedure. This one-time appointment greatly enhances the waiting time, especially when patients in high level of pain, and provides a convenient approach for the whole clinical staff. Other disease sites will be also tested with this new technology.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Multigrid Reduction in Time for Nonlinear Parabolic Problems

The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

97 MATHEMATICS AND COMPUTING↗

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↗