Results for “hybrid algorithm” — Page 54

DOE OSTI2021

Tracking the ancestry of known and ‘ghost’ homeologous subgenomes in model grass Brachypodium polyploids

Unraveling the evolution of plant polyploids is a challenge when their diploid progenitor species are extinct or unknown or when genome sequences of known progenitors are unavailable. Existing subgenome identification methods cannot adequately infer the homeologous genomes that are present in the allopolyploids if they do not take into account the potential existence of unknown progenitors. We addressed this challenge in the widely distributed dysploid grass genus Brachypodium, which is a model genus for temperate cereals and biofuel grasses. We used a transcriptome-based phylogeny and newly designed subgenome detection algorithms coupled with a comparative chromosome barcoding analysis. Our phylogenomic subgenome detection pipeline was validated in Triticum allopolyploids, which have known progenitor genomes, and then used to infer the identities of three subgenomes derived from extant diploid species and four subgenomes derived from unknown diploid progenitors (ghost subgenomes) in six Brachypodium polyploids (B. mexicanum, B. boissieri, B. retusum, B. phoenicoides, B. rupestre and B. hybridum), of which five contain undescribed homeologous subgenomes. The existence of the seven Brachypodium progenitor genomes in the polyploids was confirmed by their karyotypic barcode profiles. Comparative phylogenomics of nuclear versus plastid trees allowed us to formulate hypothetical homoploid hybridizations and allo- and autopolyploidization scenarios that could have generated the six Brachypodium polyploids.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Ab initio many-fermion structure calculations on a quantum computer

To overcome the limitations of existing algorithms for solving self-bound quantum many-body problems—such as those encountered in nuclear and particle physics—that access only a restricted subset of energy levels and provide limited structural information, we introduce and demonstrate a novel quantum-classical approach capable of resolving the complete bound-state spectrum. This method also provides the total angular momentum 𝐽 associated with each eigenstate. Here, our approach is based on expressing the Hamiltonian in second-quantized form within a novel input model combined with a scan scheme, enabling broad applicability to configuration-interaction calculations across diverse fields. We apply this hybrid method to compute, for the first time, the bound-state spectrum together with corresponding 𝐽 values of 20 O using a realistic strong-interaction Hamiltonian. Our approach applies to hadron spectra and 𝐽 values solved in the relativistic basis light-front quantization approach.

Du, Weijie [Chinese Academy of Sciences (CAS), Lan↗

NASA NTRS1992

Recognition of partially occluded threat objects using the annealed Hopefield network

Recognition of partially occluded objects has been an important issue to airport security because occlusion causes significant problems in identifying and locating objects during baggage inspection. The neural network approach is suitable for the problems in the sense that the inherent parallelism of neural networks pursues many hypotheses in parallel resulting in high computation rates. Moreover, they provide a greater degree of robustness or fault tolerance than conventional computers. The annealed Hopfield network which is derived from the mean field annealing (MFA) has been developed to find global solutions of a nonlinear system. In the study, it has been proven that the system temperature of MFA is equivalent to the gain of the sigmoid function of a Hopfield network. In our early work, we developed the hybrid Hopfield network (HHN) for fast and reliable matching. However, HHN doesn't guarantee global solutions and yields false matching under heavily occluded conditions because HHN is dependent on initial states by its nature. In this paper, we present the annealed Hopfield network (AHN) for occluded object matching problems. In AHN, the mean field theory is applied to the hybird Hopfield network in order to improve computational complexity of the annealed Hopfield network and provide reliable matching under heavily occluded conditions. AHN is slower than HHN. However, AHN provides near global solutions without initial restrictions and provides less false matching than HHN. In conclusion, a new algorithm based upon a neural network approach was developed to demonstrate the feasibility of the automated inspection of threat objects from x-ray images. The robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features.

Kim, Jung H.↗

NASA NTRS2009

Reaction Wheel Disturbance Model Extraction Software - RWDMES

The RWDMES is a tool for modeling the disturbances imparted on spacecraft by spinning reaction wheels. Reaction wheels are usually the largest disturbance source on a precision pointing spacecraft, and can be the dominating source of pointing error. Accurate knowledge of the disturbance environment is critical to accurate prediction of the pointing performance. In the past, it has been difficult to extract an accurate wheel disturbance model since the forcing mechanisms are difficult to model physically, and the forcing amplitudes are filtered by the dynamics of the reaction wheel. RWDMES captures the wheel-induced disturbances using a hybrid physical/empirical model that is extracted directly from measured forcing data. The empirical models capture the tonal forces that occur at harmonics of the spin rate, and the broadband forces that arise from random effects. The empirical forcing functions are filtered by a physical model of the wheel structure that includes spin-rate-dependent moments (gyroscopic terms). The resulting hybrid model creates a highly accurate prediction of wheel-induced forces. It accounts for variation in disturbance frequency, as well as the shifts in structural amplification by the whirl modes, as the spin rate changes. This software provides a point-and-click environment for producing accurate models with minimal user effort. Where conventional approaches may take weeks to produce a model of variable quality, RWDMES can create a demonstrably high accuracy model in two hours. The software consists of a graphical user interface (GUI) that enables the user to specify all analysis parameters, to evaluate analysis results and to iteratively refine the model. Underlying algorithms automatically extract disturbance harmonics, initialize and tune harmonic models, and initialize and tune broadband noise models. The component steps are described in the RWDMES user s guide and include: converting time domain data to waterfall PSDs (power spectral densities); converting PSDs to order analysis data; extracting harmonics; initializing and simultaneously tuning a harmonic model and a wheel structural model; initializing and tuning a broadband model; and verifying the harmonic/broadband/structural model against the measurement data. Functional operation is through a MATLAB GUI that loads test data, performs the various analyses, plots evaluation data for assessment and refinement of analysis parameters, and exports the data to documentation or downstream analysis code. The harmonic models are defined as specified functions of frequency, typically speed-squared. The reaction wheel structural model is realized as mass, damping, and stiffness matrices (typically from a finite element analysis package) with the addition of a gyroscopic forcing matrix. The broadband noise model is realized as a set of speed-dependent filters. The tuning of the combined model is performed using nonlinear least squares techniques. RWDMES is implemented as a MATLAB toolbox comprising the Fit Manager for performing the model extraction, Data Manager for managing input data and output models, the Gyro Manager for modifying wheel structural models, and the Harmonic Editor for evaluating and tuning harmonic models. This software was validated using data from Goodrich E wheels, and from GSFC Lunar Reconnaissance Orbiter (LRO) wheels. The validation testing proved that RWDMES has the capability to extract accurate disturbance models from flight reaction wheels with minimal user effort.

Blaurock, Carl↗

NASA NTRSDate not supplied

Transient Optimization of an Electrified Gas Turbine Engine Using Machine Learning

Gas turbine engines are designed with sufficient margin to prevent stall under normal operating conditions throughout their life. This compromise ensures that during rapid accelerations, compressor operation remains stable, but at the cost of efficiency and thrust responsiveness. The design margin encompasses multiple sources of uncertainty and systematic deviances from the operating line, the largest of which is the transient allowance. This set-aside accounts for the temporary incoordination of the engine spools during an acceleration while still enabling it to meet the certification requirement to accelerate from low to high power within a specified time, and without experiencing overtemperature, surge, stall, or other detrimental factors. Electrification of the powertrain provides the opportunity to address this reserve and truly optimize the design. The addition of electric machines inherent in hybrid propulsion concepts offers a means to interact with the engine shafts such that the necessary margin can be reduced, which can positively impact the engine design. By adjusting the amount of power extracted from or injected to the engine spools by the electric machines during transient operation, excursions from the operating line can be minimized. Past work using a dynamic engine model has shown that optimization of the fuel flow schedule during acceleration can reduce the required margin while still meeting the time requirement, and results are further improved when combined with power injection and extraction. The current work uses machine learning through a genetic algorithm to address the problem holistically by concurrently optimizing the electric machine power command and fuel flow acceleration schedule using an updated, higher fidelity version of the original engine model.

Stall Margin↗

NASA NTRSDate not supplied

Transient Optimization of an Electrified Gas Turbine Engine Using Machine Learning

Gas turbine engines are designed with sufficient margin to prevent stall under normal operating conditions throughout their life. This compromise ensures that during rapid accelerations, compressor operation remains stable, but at the cost of efficiency and thrust responsiveness. The design margin encompasses multiple sources of uncertainty and systematic deviances from the operating line, the largest of which is the transient allowance. This set-aside accounts for the temporary incoordination of the engine spools during an acceleration while still enabling it to meet the certification requirement to accelerate from low to high power within a specified time, and without experiencing overtemperature, surge, stall, or other detrimental factors. Electrification of the powertrain provides the opportunity to address this reserve and truly optimize the design. The addition of electric machines inherent in hybrid propulsion concepts offers a means to interact with the engine shafts such that the necessary margin can be reduced, which can positively impact the engine design. By adjusting the amount of power extracted from or injected to the engine spools by the electric machines during transient operation, excursions from the operating line can be minimized. Past work using a dynamic engine model has shown that optimization of the fuel flow schedule during acceleration can reduce the required margin while still meeting the time requirement, and results are further improved when combined with power injection and extraction. The current work uses machine learning through a genetic algorithm to address the problem holistically by concurrently optimizing the electric machine power command and fuel flow acceleration schedule using an updated, higher fidelity version of the original engine model.

Stall Margin↗

NASA NTRS2024

Transient Optimization of an Electrified Gas Turbine Engine Using Machine Learning

Gas turbine engines are designed with sufficient margin to prevent stall under normal operating conditions throughout their life. This compromise ensures that during rapid accelerations, compressor operation remains stable, but at the cost of efficiency and thrust responsiveness. The design margin encompasses multiple sources of uncertainty and systematic deviances from the operating line, the largest of which is the transient allowance. This set-aside accounts for the temporary incoordination of the engine spools during an acceleration while still enabling it to meet the certification requirement to accelerate from low to high power within a specified time, and without experiencing overtemperature, surge, stall, or other detrimental factors. Electrification of the powertrain provides the opportunity to address this reserve and truly optimize the design. The addition of electric machines inherent in hybrid propulsion concepts offers a means to interact with the engine shafts such that the necessary margin can be reduced, which can positively impact the engine design. By adjusting the amount of power extracted from or injected to the engine spools by the electric machines during transient operation, excursions from the operating line can be minimized. Past work using a dynamic engine model has shown that optimization of the fuel flow schedule during acceleration can reduce the required margin while still meeting the time requirement, and results are further improved when combined with power injection and extraction. The current work uses machine learning through a genetic algorithm to address the problem holistically by concurrently optimizing the electric machine power command and fuel flow acceleration schedule using an updated, higher fidelity version of the original engine model.

Stall Margin↗

NASA NTRS2002

Bioinspired engineering of exploration systems for NASA and DoD

A new approach called bioinspired engineering of exploration systems (BEES) and its value for solving pressing NASA and DoD needs are described. Insects (for example honeybees and dragonflies) cope remarkably well with their world, despite possessing a brain containing less than 0.01% as many neurons as the human brain. Although most insects have immobile eyes with fixed focus optics and lack stereo vision, they use a number of ingenious, computationally simple strategies for perceiving their world in three dimensions and navigating successfully within it. We are distilling selected insect-inspired strategies to obtain novel solutions for navigation, hazard avoidance, altitude hold, stable flight, terrain following, and gentle deployment of payload. Such functionality provides potential solutions for future autonomous robotic space and planetary explorers. A BEES approach to developing lightweight low-power autonomous flight systems should be useful for flight control of such biomorphic flyers for both NASA and DoD needs. Recent biological studies of mammalian retinas confirm that representations of multiple features of the visual world are systematically parsed and processed in parallel. Features are mapped to a stack of cellular strata within the retina. Each of these representations can be efficiently modeled in semiconductor cellular nonlinear network (CNN) chips. We describe recent breakthroughs in exploring the feasibility of the unique blending of insect strategies of navigation with mammalian visual search, pattern recognition, and image understanding into hybrid biomorphic flyers for future planetary and terrestrial applications. We describe a few future mission scenarios for Mars exploration, uniquely enabled by these newly developed biomorphic flyers.

Space Flight↗

DOE OSTI2022

Quantum algorithm for electronic band structures with local tight-binding orbitals

While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

BEYONDPLANCK IV. On end-to-end simulations in CMB analysis — Bayesian versus frequentist statistics

End-to-end simulations play a key role in the analysis of any high-sensitivity cosmic microwave background (CMB) experiment, providing high-fidelity systematic error propagation capabilities that are unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely, how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data or as a random realization independent from the data. We refer to these as posterior and prior simulations, respectively. We show that the two options lead to significantly different correlation structures, as prior simulations (contrary to posterior simulations) effectively include cosmic variance, but they exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties. We argue that as a result, they also have different and complementary scientific uses, even if this dichotomy is not absolute. In particular, posterior simulations are in general more convenient for parameter estimation studies, while prior simulations are generally more convenient for model testing. Before BEYONDPLANCK, most pipelines used a mix of constrained and random inputs and applied the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. BEYONDPLANCK represents the first end-to-end CMB simulation framework that is able to generate both types of simulations and these new capabilities have brought this topic to the forefront. The BEYONDPLANCK posterior simulations and their uses are described extensively in a suite of companion papers. In this work, we consider one important applications of the corresponding prior simulations, namely, code validation. Specifically, we generated a set of one-year LFI 30 GHz prior simulations with known inputs and we used these to validate the core low-level BEYONDPLANCK algorithms dealing with gain estimation, correlated noise estimation, and mapmaking.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2019

AERONET Remotely Sensed Measurements and Retrievals of Biomass Burning Aerosol Optical Properties During the 2015 Indonesian Burning Season

An extreme biomass-burning event occurred in Indonesia from September through October 2015 due to severe drought conditions, partially caused by a major El Nino event, thereby allowing for significant burning of peatland that had been previously drained. This event had the highest sustained aerosol optical depths (AOD) ever monitored by the global Aerosol Robotic Network (AERONET). The newly developed AERONET Version 3 algorithms retain high AOD at the longer wavelengths when associated with high Angstrom Exponents (AEs), which thereby allowed for measurements of AOD at 675 nanometers as high as approximately 7, the upper limit of Sun photometry. Measured AEs at the highest monitored AOD levels were subsequently utilized to estimate instantaneous values of AOD at 550 nanometers in the range of 11 to 13, well beyond the upper measurement limit. Additionally, retrievals of complex refractive indices, size distributions, and single scattering albedos (SSA) were obtained at much higher AOD levels than possible from almucantar scans due to the ability to perform retrievals at smaller solar zenith angles with new hybrid sky radiance scans. For retrievals made at the highest AOD levels the fine mode volume median radii were approximately 0.25 to 0.30 microns, which are very large particles for biomass burning. Very high SSA values (approximately 0.975 from 440 to 1020 nanometers) are consistent with the domination by smoldering combustion of peat burning. Estimates of the percentage peat contribution to total biomass burning aerosol based on retrieved SSA and laboratory measured peat SSA were approximately 80-85 percent, in excellent agreement with independent estimates.

Eck, T. F.↗

NASA NTRS2018

Hybrid Lyot Coronagraph for WFIRST: High Contrast Testbed Demonstration in Flight-like Low Flux Environment

In order to validate required operation of the proposed Wide-Field InfraRed Survey Telescope (WFIRST) coronagraph instrument, we have built a testbed in Jet Propulsion Laboratory (JPL), which is analogous to the baseline WFIRST coronagraph instrument architecture. Since its birth in 2016, this testbed, named as Occulting Mask Coronagraph (OMC) testbed, has demonstrated several crucial technological milestones: Broadband high contrast demonstration in both Hybrid Lyot Coronagraph (HLC) and Shape Pupil Coronagraph (SPC) modes while the Low Order Wavefront Sensing and Control (LOWFS/C) subsystem senses and corrects the dynamic ﬂight-like wavefront disturbances. In this paper, we present up-to-date progress of HLC mode demonstration in the OMC testbed. While injecting the ﬂight-like low photon ﬂux starlight with expected Line of Sight (LoS) and Wavefront Error (WFE) perturbation to the OMC testbed, we demonstrate generating high contrast dark hole images. We ﬁrst study the expected photon ﬂux in actual ﬂight environment, and estimate detection noise and estimation accuracy of the complex electric ﬁeld if the wavefront sensing algorithm is used based on the pair-wise diﬀerence imaging. Then, we introduce our improved scheme to mitigate this photon-starved ﬂight-like low ﬂux environment. As a result, we generate a dark hole that meets the WFIRST raw contrast requirements using the 2nd magnitude star light. We establish the key ideas, describe test setups, and demonstrate test results with data analysis.

Wilson, Daniel↗

NASA NTRS2024

Evaluation of Machine Learning and Deep Learning Algorithms for Fire Prediction in Southeast Asia

Vegetation fires are prevalent in South/Southeast Asian countries, making fire prediction crucial due to their potential environmental, economic, and social impacts. Accurate predictions of fires facilitate timely interventions, helping to mitigate uncontrolled fires that can lead to biodiversity loss and air quality issues. In this study, we utilize VIIRS satellite-derived fire data alongside six machine learning and deep learning models—Simple Persistence, Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), CNN-LSTM, and ConvLSTM—to determine the most effective fire prediction model, using Root Mean Square Error (RMSE) as the metric. Our results indicate that the CNN model is the most reliable in regions with spatial dependencies, such as Brunei, Indonesia, Malaysia, the Philippines, Timor-Leste, and Thailand. Conversely, the ConvLSTM model excels in countries with complex spatiotemporal dynamics like Laos, Myanmar, and Vietnam. The CNN-LSTM hybrid model also performed well in Cambodia, suggesting a need for a balanced approach in areas requiring both spatial and temporal feature extraction. Furthermore, simpler models like Persistence and MLP showed limitations in capturing dynamic patterns and temporal dependencies. Our findings highlight the importance of evaluating models before implementing any decision support systems (DSS) in fire management. By tailoring models to specific regional fire data, we can enhance prediction accuracy and responsiveness, ultimately improving fire risk management in Southeast Asia and beyond.

Deep learning↗

DOE OSTI2022

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2007

NavP: Structured and Multithreaded Distributed Parallel Programming

We present Navigational Programming (NavP) -- a distributed parallel programming methodology based on the principles of migrating computations and multithreading. The four major steps of NavP are: (1) Distribute the data using the data communication pattern in a given algorithm; (2) Insert navigational commands for the computation to migrate and follow large-sized distributed data; (3) Cut the sequential migrating thread and construct a mobile pipeline; and (4) Loop back for refinement. NavP is significantly different from the current prevailing Message Passing (MP) approach. The advantages of NavP include: (1) NavP is structured distributed programming and it does not change the code structure of an original algorithm. This is in sharp contrast to MP as MP implementations in general do not resemble the original sequential code; (2) NavP implementations are always competitive with the best MPI implementations in terms of performance. Approaches such as DSM or HPF have failed to deliver satisfying performance as of today in contrast, even if they are relatively easy to use compared to MP; (3) NavP provides incremental parallelization, which is beyond the reach of MP; and (4) NavP is a unifying approach that allows us to exploit both fine- (multithreading on shared memory) and coarse- (pipelined tasks on distributed memory) grained parallelism. This is in contrast to the currently popular hybrid use of MP+OpenMP, which is known to be complex to use. We present experimental results that demonstrate the effectiveness of NavP.

navigational programming (NavP)↗

DOE OSTI2022

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Furthermore, our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

25 ENERGY STORAGE↗

DOE OSTI2023

Analysis and mitigation of an oscillating background on hybrid complementary metal-oxide semiconductor (hCMOS) imaging sensors at the National Ignition Facility

Nanosecond-gated hybrid complementary metal-oxide semiconductor imaging sensors are a powerful tool for temporally gated and spatially resolved measurements in high energy density science, including inertial confinement fusion, and in laser diagnostics. However, a significant oscillating background excited by photocurrent has been observed in image sequences during testing and in experiments at the National Ignition Facility (NIF). Characterization measurements and simulation results are used to explain the oscillations as the convolution of the pixel-level sensor response with a sensor-wide RLC circuit ringing. Finally, data correction techniques are discussed for NIF diagnostics, and for diagnostics where these techniques cannot be used, a proof-of-principle image correction algorithm is presented.

42 ENGINEERING↗

NASA NTRS1994

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗