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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Bayesian estimation of crack initiation times from service data

Lockheed C-130 Hercules aircraft have during their service life been periodically inspected and growing cracks around rivet holes were recorded. This record has recently been used to determine the statistical distributions of crack initiation times and the distribution of initial crack sizes. When crack initiation times are calculated from such cracks, by backward extrapolation of the growth relation, the resulting distribution of crack initiation times will indicate a preponderance of short times to crack initiation. If however, such distributions are combined with the reliability of the inspection procedure, the statistical distribution of missed initiation times can be estimated. The method used is based on Bayes theorem which permits the calculation of the 'prior' distribution (initiation times before inspection) from a knowledge of the 'posterior' distribution (initiation times obtained from the inspection) and a 'likelihood function' (reliability of the inspection) procedure. The results indicate that during an early inspection a large percentage of initiation times will be missed and that the fraction of located initiation times increases during later inspections.

Heller, R. A.↗
NASA NTRS1981

Time elements in Keplerian orbital elements

Time elements are introduced in terms of Keplerian (classical) orbital elements for use with time transformations of the Sundman type. Three different time elements are introduced. One time element is associated with the eccentric anomaly, a second time element is associated with the true anomaly, and a third time element is associated with the intermediate anomaly. Numerical results are presented that show accuracy improvements of from one to two orders of magnitude when time elements are employed along with Sundman time transformations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1984

Comparison of frequency-domain and time-domain rotorcraft vibration control methods

Active control of rotor-induced vibration in rotorcraft has received significant attention recently. Two classes of techniques have been proposed. The more developed approach works with harmonic analysis of measured time histories and is called the frequency-domain approach. The more recent approach computes the control input directly using the measured time history data and is called the time-domain approach. The report summarizes the results of a theoretical investigation to compare the two approaches. Five specific areas were addressed: (1) techniques to derive models needed for control design (system identification methods), (2) robustness with respect to errors, (3) transient response, (4) susceptibility to noise, and (5) implementation difficulties. The system identification methods are more difficult for the time-domain models. The time-domain approach is more robust (e.g., has higher gain and phase margins) than the frequency-domain approach. It might thus be possible to avoid doing real-time system identification in the time-domain approach by storing models at a number of flight conditions. The most significant error source is the variation in open-loop vibrations caused by pilot inputs, maneuvers or gusts. The implementation requirements are similar except that the time-domain approach can be much simpler to implement if real-time system identification were not necessary.

Gupta, N. K.↗
NASA NTRS1986

Methane oxidation behind reflected shock waves: Ignition delay times measured by pressure and flame band emission

Ignition delay data were recorded for three methane-oxygen-argon mixtures (phi = 0.5, 1.0, 2.0) for the temperature range 1500 to 1920 K. Quiet pressure trances enabled us to obtain delay times for the start of the experimental pressure rise. These times were in good agreement with those obtained from the flame band emission at 3700 A. The data correlated well with the oxygen and methane dependence of Lifshitz, but showed a much stronger temperature dependence (phi = 0.5 delta E = 51.9, phi = 1.0 delta = 58.8, phi = 2.0 delta E = 58.7 Kcal). The effect of probe location on the delay time measurement was studied. It appears that the probe located 83 mm from the reflecting surface measured delay times which may not be related to the initial temperature and pressure. It was estimated that for a probe located 7 mm from the reflecting surface, the measured delay time would be about 10 microseconds too short, and it was suggested that delay times less than 100 microsecond should not be used. The ignition period was defined as the time interval between start of the experimental pressure rise and 50 percent of the ignition pressure. This time interval was measured for three gas mixtures and found to be similar (40 to 60 micro sec) for phi = 1.0 and 0.5 but much longer (100 to 120) microsecond for phi = 2.0. It was suggested that the ignition period would be very useful to the kinetic modeler in judging the agreement between experimental and calculated delay times.

Brabbs, T. A.↗
NASA NTRS1987

Results of using the global positioning system to maintain the time and frequency synchronization in the Deep Space Network

There are two hydrogen maser clocks located at each signal processing center (SPC) in the DSN. Close coordination of the time and frequency of the SPC clocks is needed to navigate spacecraft to the outer planets. A recent example was the Voyager spacecraft's encounter with Uranus in January 1986. The clocks were adjusted with the goal of minimizing time and frequency offsets between the SPCs at encounter. How time and frequency at each SPC is estimated using data acquired from the Global Positioning System Timing Receivers operating on the NBS-BIH (National Bureau of Standards-Bureau International de l'Heure) tracking schedule is described. These data are combined with other available timing receiver data to calculate the time offset estimates. The adjustment of the clocks is described. It was determined that long range hydrogen maser drift is quite predictable and adjustable within limits. This enables one to minimize time and frequency differences between the three SPCs for many months by matching the drift rates of the three standards. Data acquisition and processing techniques using a Kalman filter to make estimates of time and frequency offsets between the clocks at the SPCs and UTC(NBS) (Coordinated Universal Time realized at NBS) are described.

Clements, P. A.↗
NASA NTRS1987

Piloted simulator study of allowable time delay in pitch flight control system of a transport airplane with negative static stability

A piloted simulation study was conducted to determine the permissible time delay in the flight control system of a 10-percent statically unstable transport airplane during cruise flight conditions. The math model used for the simulation was a derivative Lockheed L-1011 wide-body jet transport. Data were collected and analyzed from a total of 137 cruising flights in both calm- and turbulent-air conditions. Results of this piloted simulation study verify previous findings that show present military specifications for allowable control-system time delay may be too stringent when applied to transport-size airplanes. Also, the degree of handling-qualities degradation due to time delay is shown to be strongly dependent on the source of the time delay in an advanced flight control system. Maximum allowable time delay for each source of time delay in the control system, in addition to a less stringent overall maximum level of time delay, should be considered for large aircraft. Preliminary results also suggest that adverse effects of control-system time delay may be at least partially offset by variations in control gearing. It is recommended that the data base include different airplane baselines, control systems, and piloting tasks with many pilots participating, so that a reasonable set of limits for control-system time delay can be established to replace the military specification limits currently being used.

Grantham, William D.↗
NASA NTRS1993

Teaching high-performance skills using above-real-time training

The above real-time training (ARTT) concept is an approach to teaching high-performance skills. ARTT refers to a training paradigm that places the operator in a simulated environment that functions at faster than normal time. It represents a departure from the intuitive, but not often supported, feeling that the best practice is determined by the training environment with the highest fidelity. This approach is hypothesized to provide greater 'transfer value' per simulation trial, by incorporating training techniques and instructional features into the simulator. Two related experiments are discussed. In the first, 25 naive male subjects performed three tank gunnery tasks on a simulator under varying levels of time acceleration (i.e., 1.0x, 1.6x, 2.0x, sequential, and mixed). They were then transferred to a standard (1.0x) condition for testing. Every accelerated condition or combination of conditions produced better training and transfer than the standard condition. Most effective was the presentation of trials at 1.0x, 1.6x, and 2.0x in a random order during training. Overall, the best ARTT group scored about 50 percent higher and trained in 25 percent less time compared to the real-time control group. In the second experiment, 24 mission-capable F-16 pilots performed three tasks on a part-task F-16A flight simulator under varying levels of time compression (i.e., 1.0x, 1.5x, 2.0x, and random). All subjects were then tested in a real-time environment. The emergency procedure (EP) task results showed increased accuracy for the ARTT groups. In testing (transfer), the ARTT groups not only performed the EP more accurately, but dealt with a simultaneous enemy significantly better than a real-time control group. Although the findings on an air combat maneuvering task and stern conversion task were mixed, most measures indicated that the ARTT groups performed better and faster than a real-time control group. Other implications for ARTT are discussed along with future research directions.

Guckenberger, Dutch↗
NASA NTRS1993

Time dependent turbulence modeling and analytical theories of turbulence

By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.

Rubinstein, R.↗
NASA NTRS1994

The two-way time synchronization system via a satellite voice channel

A newly developed two-way time synchronization system is described in this paper. The system uses one voice channel at a SCPC satellite digital communication earth station, whose bandwidth is only 45 kHz, thus saving satellite resources greatly. The system is composed of one master station and one or several, up to sixty-two, secondary stations. The master and secondary stations are equipped with the same equipment, including a set of timing equipment, a synthetic data terminal for time synchronizing, and a interface unit between the data terminal and the satellite earth station. The synthetic data terminal for time synchronization also has an IRIG-B code generator and a translator. The data terminal of master station is the key part of whole system. The system synchronization process is full automatic, which is controlled by the master station. Employing an autoscanning technique and conversational mode, the system accomplishes the following tasks: linking up liaison with each secondary station in turn, establishing a coarse time synchronization, calibrating date (years, months, days) and time of day (hours, minutes, seconds), precisely measuring the time difference between local station and the opposite station, exchanging measurement data, statistically processing the data, rejecting error terms, printing the data, calculating the clock difference and correcting the phase, thus realizing real-time synchronization from one point to multiple points. We also designed an adaptive phase circuit to eliminate the phase ambiguity of the PSK demodulator. The experiments have shown that the time synchronization accuracy is better than 2 mu S. The system has been put into regular operation.

Heng-Qiu, Zheng↗
NASA NTRS1994

A combined algorithm for minimum time slewing of flexible spacecraft

The use of Pontryagin's Maximum Principle for the large-angle slewing of large flexible structures usually results in the so-called two-point boundary-value problem (TPBVP), in which many requirements (e.g., minimum time, small flexible amplitude, and limited control powers, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical computational algorithm. There are many candidate algorithms available for his problem (e.g., quasilinearization, gradient, and shooting, etc.). In this paper, a proposed algorithm, which combines the quasilinearization method with a time shortening technique and a shooting method, is applied to the minimum-time, three-dimensional, and large-angle maneuver of flexible spacecraft, particularly the orbiting Spacecraft Control Laboratory Experiment (SCOLE) configuration. Theoretically, the nonlinear TPBVP can be solved only through the shooting method to find the 'exact' switching times for the bang-bang controls. However, computationally, a suitable guess for the missing initial costates is crucial because the convergence range of the unknown initial costates is usually narrow, especially for systems with high dimensions and when a multi-bang-bang control strategy is needed. On the other hand, the problems of near minimum time attitude maneuver of general rigid spacecraft and fast slewing of flexible spacecraft have been examined by the authors through a numerical approach based on the quasilinearization algorithm with a time shortening technique. Computational results have demonstrated its broad convergence range and insensitivity to initial costate choices. Consequently, a combined approach is naturally suggested here to solve the minimum time slewing problem. That is, in the computational process, the quasilinearization method is used first to obtain a near minimum time solution. Then, the acquired converged initial costates from the quasilinearization approach are transformed (tailored) to and used as the initial costate guess for starting the shooting method. Finally, the shooting method takes over the remaining calculations until the minimum-time solution converges. The nonlinear equations of motion of the SCOLE are formulated by using Lagrange's equations, with the mast modeled as a continuous beam subject to three-dimensional deformations. The numerical results will be presented and some related computational issues will also be discussed.

Bainum, P. M.↗
NASA NTRS1995

Network time synchronization servers at the US Naval Observatory

Responding to an increased demand for reliable, accurate time on the Internet and Milnet, the U.S. Naval Observatory Time Service has established the network time servers, tick.usno.navy.mil and tock.usno.navy.mil. The system clocks of these HP9000/747i industrial work stations are synchronized to within a few tens of microseconds of USNO Master Clock 2 using VMEbus IRIG-B interfaces. Redundant time code is available from a VMEbus GPS receiver. UTC(USNO) is provided over the network via a number of protocols, including the Network Time Protocol (NTP) (DARPA Network Working Group Report RFC-1305), the Daytime Protocol (RFC-867), and the Time protocol (RFC-868). Access to USNO network time services is presently open and unrestricted. An overview of USNO time services and results of LAN and WAN time synchronization tests will be presented.

Schmidt, Richard E.↗
NASA NTRS1993

Time-dependent modulation of galactic cosmic rays by merged interaction regions

Models that solve the one-dimensional, solar modulation equation have reproduced the 11-year galactic cosmic ray using functional representations of global merged interaction regions (MIRs). This study extends those results to the solution of the modulation equation with explicit time dependence. The magnetometers on Voyagers 1 and 2 provide local magnetic field intensities at regular intervals, from which one calculates the ratio of the field intensity to the average local field. These ratios in turn are inverted to form diffusion coefficients. Strung together in radius and time, these coefficents then fall and rise with the strength of the interplanetary magnetic field, becoming representations of MIRs. These diffusion coefficients, calculated locally, propagate unchanged from approx. 10 AU to the outer boundary (120 AU). Inside 10 AU, all parameters, including the diffusion coefficient are assumed constant in time and space. The model reproduces the time-intensity profiles of Voyager 2 and Pioneer 10. Radial gradient data from 1982-1990 between Pioneer 10 and Voyager 2 are about the same magnitude as those calculated in the model. It is also shows agreement in rough magnitude with the radial gradient between Pioneer 10 and 1 AU. When coupled with enhanced, time-dependent solar wind speed at the probe's high latitude, as measured by independent observers, the model also follows Voyager 1's time-intensity profile reasonably well, providing a natural source the model also follows Voyager 1's time-intensity profile reasonably well, providing a natural source for the observed negative latitudinal gradients. The model exhibits the 11-year cyclical cosmic ray intensity behavior at all radii, including 1 AU, not just at the location of the spacecraft where the magnetic fields are measured. In addition, the model's point of cosmic ray maximum correctly travels at the solar wind speed, illustrating the well-known propagation of modulation. Finally, at least in the inner heliosphere this model accounts for the delay experienced by lower-rigidity protons in reaching their time-intensity peak. The actual delays in this model, however, are somewhat smaller than the data. In the outer heliosphere the models sees no delays, and the data are ambiguous as to their existence. It appears that strong magnetic field compression regions (merged interaction regions) that are 3-4 times the average field strength can, at least in a helioequatorial band, disrupt effects, such as drifts, that could dominate in quieter magnetic fields. The question remains: Is the heliosphere ever quiet enough to allow such effects to be unambiguously measured, at least in the midlatitudes?

Perko, J. S.↗
NASA NTRS2000

Scheduling and Estimating the Cost of Crew Time

In a previous paper, Theory and Application of the Equivalent System Mass Metric, Julie Levri, David Vaccari, and Alan Drysdale developed a method for computing the Equivalent System Mass (ESM) of crew time. ESM is an analog of cost. The suggested approach has been applied but seems to impose too high a cost for small additional requirements for crew time. The proposed method is based on the minimum average cost of crew time. In this work, the scheduling of crew time is examined in more detail, using suggested crew time allocations and daily work schedules. Crew tasks are typically assigned using priorities, which can also be used to construct a crew time demand curve mapping the value or cost per hour versus the total number of hours worked. The cost of additional crew time can be estimated by considering the intersection and shapes of the demand and supply curves. If e assume a mathematical form for the demand curve, a revised method can be developed for computing the cost or ESM of crew time. This method indicates a low cost per hour for small additional requirements for crew time and an increasing cost per hour for larger requirements.

Jones, Harry↗
NASA NTRS1998

A Fast-Time Study of Aircraft Reordering in Arrival Sequencing and Scheduling

In order to ensure that the safe capacity of the terminal area is not exceeded, Air Traffic Management ATM often places restrictions on arriving flights transitioning from en route airspace to terminal airspace. This restriction of arrival traffic is commonly referred to as arrival flow management, and includes techniques such as metering, vectoring, fix-load balancing, and the imposition of miles-in-trail separations. These restrictions are enacted without regard for the relative priority which airlines may be placing on individual flights based on factors such as crew criticality, passenger connectivity, critical turn times, gate availability, on-time performance, fuel status, or runway preference. The development of new arrival flow management techniques which take into consideration priorities expressed by air carriers will likely reduce the economic impact of ATM restrictions on the airlines and lead to increased airline economic efficiency by allowing airlines to have greater control over their individual arrival banks of aircraft. NASA and the Federal Aviation Administration (FAA) have designed and developed a suite of software decision support tools (DSTs) collectively known as the Center TRACON Automation System (CTAS). One of these tools, the Traffic Management Advisor (TMA) is currently being used at the Fort Worth Air Route Traffic Control Center to perform arrival flow management of traffic into the Dallas/Fort Worth airport (DFW). The TMA is a time-based strategic planning tool that assists Traffic Management Coordinators (TMCs) and En Route Air Traffic Controllers in efficiently balancing arrival demand with airport capacity. The primary algorithm in the TMA is a real-time scheduler which generates efficient landing sequences and landing times for arrivals within about 200 no a. from touchdown. This scheduler will sequence aircraft so that they arrive in a first- come - first-served (FCFS) order. While FCFS sequencing establishes a fair order based on estimated times of arrival, it does not take into account individual airline priorities among incoming flights. NASA is exploring the possibility of allowing airlines to express relative arrival priorities to air traffic management through the development of new CTAS scheduling algorithms which take into consideration airline arrival preferences. The accommodation of airline priorities in arrival sequencing and scheduling would under most circumstances result in a deviation from a "natural" or FCFS arrival order. As a First step toward developing airline influenced sequencing algorithms, an investigation was conducted to determine the feasibility of reordering arrival traffic from a strict FCFS sequence. A fast-time simulation has been developed which allows statistical evaluation of sequencing and scheduling algorithms for arrival traffic at the Dallas/Fort Worth Airport. In contrast to real-time simulation or field tests, which would require on the order of ninety minutes to examine a single traffic rush period, the fast-time simulation allows examination of multiple rush periods in a matter of seconds.

Carr, Greg↗
NASA NTRS2003

Real-time three-dimensional color doppler evaluation of the flow convergence zone for quantification of mitral regurgitation: Validation experimental animal study and initial clinical experience

BACKGROUND: Pitfalls of the flow convergence (FC) method, including 2-dimensional imaging of the 3-dimensional (3D) geometry of the FC surface, can lead to erroneous quantification of mitral regurgitation (MR). This limitation may be mitigated by the use of real-time 3D color Doppler echocardiography (CE). Our objective was to validate a real-time 3D navigation method for MR quantification. METHODS: In 12 sheep with surgically induced chronic MR, 37 different hemodynamic conditions were studied with real-time 3DCE. Using real-time 3D navigation, the radius of the largest hemispherical FC zone was located and measured. MR volume was quantified according to the FC method after observing the shape of FC in 3D space. Aortic and mitral electromagnetic flow probes and meters were balanced against each other to determine reference MR volume. As an initial clinical application study, 22 patients with chronic MR were also studied with this real-time 3DCE-FC method. Left ventricular (LV) outflow tract automated cardiac flow measurement (Toshiba Corp, Tokyo, Japan) and real-time 3D LV stroke volume were used to quantify the reference MR volume (MR volume = 3DLV stroke volume - automated cardiac flow measurement). RESULTS: In the sheep model, a good correlation and agreement was seen between MR volume by real-time 3DCE and electromagnetic (y = 0.77x + 1.48, r = 0.87, P <.001, delta = -0.91 +/- 2.65 mL). In patients, real-time 3DCE-derived MR volume also showed a good correlation and agreement with the reference method (y = 0.89x - 0.38, r = 0.93, P <.001, delta = -4.8 +/- 7.6 mL). CONCLUSIONS: real-time 3DCE can capture the entire FC image, permitting geometrical recognition of the FC zone geometry and reliable MR quantification.

Validation Studies↗
NASA NTRS2006

Remote Sensing Time Series Product Tool

The TSPT (Time Series Product Tool) software was custom-designed for NASA to rapidly create and display single-band and band-combination time series, such as NDVI (Normalized Difference Vegetation Index) images, for wide-area crop surveillance and for other time-critical applications. The TSPT, developed in MATLAB, allows users to create and display various MODIS (Moderate Resolution Imaging Spectroradiometer) or simulated VIIRS (Visible/Infrared Imager Radiometer Suite) products as single images, as time series plots at a selected location, or as temporally processed image videos. Manually creating these types of products is extremely labor intensive; however, the TSPT development tool makes the process simplified and efficient. MODIS is ideal for monitoring large crop areas because of its wide swath (2330 km), its relatively small ground sample distance (250 m), and its high temporal revisit time (twice daily). Furthermore, because MODIS imagery is acquired daily, rapid changes in vegetative health can potentially be detected. The new TSPT technology provides users with the ability to temporally process high-revisit-rate satellite imagery, such as that acquired from MODIS and from its successor, the VIIRS. The TSPT features the important capability of fusing data from both MODIS instruments onboard the Terra and Aqua satellites, which drastically improves cloud statistics. With the TSPT, MODIS metadata is used to find and optionally remove bad and suspect data. Noise removal and temporal processing techniques allow users to create low-noise time series plots and image videos and to select settings and thresholds that tailor particular output products. The TSPT GUI (graphical user interface) provides an interactive environment for crafting what-if scenarios by enabling a user to repeat product generation using different settings and thresholds. The TSPT Application Programming Interface provides more fine-tuned control of product generation, allowing experienced programmers to bypass the GUI and to create more user-specific output products, such as comparison time plots or images. This type of time series analysis tool for remotely sensed imagery could be the basis of a large-area vegetation surveillance system. The TSPT has been used to generate NDVI time series over growing seasons in California and Argentina and for hurricane events, such as Hurricane Katrina.

Predos, Don↗
NASA NTRS2008

Effect of Microstructure on Time Dependent Fatigue Crack Growth Behavior In a P/M Turbine Disk Alloy

A study was conducted to determine the processes which govern hold time crack growth behavior in the LSHR disk P/M superalloy. Nineteen different heat treatments of this alloy were evaluated by systematically controlling the cooling rate from the supersolvus solutioning step and applying various single and double step aging treatments. The resulting hold time crack growth rates varied by more than two orders of magnitude. It was shown that the associated stress relaxation behavior for these heat treatments was closely correlated with the crack growth behavior. As stress relaxation increased, the hold time crack growth resistance was also increased. The size of the tertiary gamma' in the general microstructure was found to be the key microstructural variable controlling both the hold time crack growth behavior and stress relaxation. No relationship between the presence of grain boundary M23C6 carbides and hold time crack growth was identified which further brings into question the importance of the grain boundary phases in determining hold time crack growth behavior. The linear elastic fracture mechanics parameter, Kmax, is unable to account for visco-plastic redistribution of the crack tip stress field during hold times and thus is inadequate for correlating time dependent crack growth data. A novel methodology was developed which captures the intrinsic crack driving force and was able to collapse hold time crack growth data onto a single curve.

Telesman, Ignacy J.↗
NASA NTRS2014

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

Nielsen, Tanner B.↗