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At least 73 records · Page 4

Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings

In engineering and aerospace applications, it is vital to operational success to have insight into the expected performance and health of physical systems. The field of prognostics and health management provides quantitative methods for monitoring, predicting, and managing system health. Prognostics algorithms can be employed to assess the current state of a system, propagate the system throughout time, and predict potential anomalies or failures that may occur. While they can provide accurate prediction results, effective prognostics algorithms can be challenging to use in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for future remaining useful life predictions. In this work, we implement new algorithmic approaches for prediction, quantitatively compare them via a battery degradation use-case, and provide recommendations of potential improvements to a prognostics framework. One approach to prediction is through sampling, whereby the current state of a physical system is sampled many times and each sample is propagated forward until failure is reached, resulting in a distribution of failure values. To improve the efficiency of this process, we implemented five new algorithmic approaches to prediction, including three distinct sampling methods (standard Monte Carlo, Quasi-Monte Carlo, and Latin Hypercube Sampling), a variable time step algorithm, and a variable sample size algorithm. To compare the algorithms, we employ a variety of metrics designed specifically to analyze both computational efficiency and model accuracy. Our metrics include accuracy to compare the average predicted value to ground truth, mean absolute deviation to illustrate dispersion, specific percentile error to describe accuracy within a user-defined risk tolerance, and code run-time. To quantitatively analyze our results, we employ a use-case of degradation of a Lithium-ion battery. We use an electrochemistry-based model to describe the current health state of the battery, and implement our prediction algorithms to propagate forward in time until end-of-discharge (EOD) is reached. Notably, through this work it was found that none of our sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. We find that while the sampling methods are unique, the distributions they generate are similar, ultimately producing final predictions that are nearly identical. In exploring the effect of the time step within the prediction algorithm, we found that prediction accuracy was highly dependent on the time step used, and that implementing a variable time step within a particular prediction may provide an increase in computational efficiency while also maintaining prediction accuracy. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment can result in improved computation speed and maintained prediction accuracy. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency.

prognostics

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics

Performance tests of signature extension algorithms

Comparative tests were performed on seven signature extension algorithms to evaluate their effectiveness in correcting for changes in atmospheric haze and sun angle in a Landsat scene. Four of the algorithms were cluster matching, and two were maximum likelihood algorithms. The seventh algorithm determined the haze level in both training and recognition segments and used a set of tables calculated from an atmospheric model to determine the affine transformation that corrects the training signatures for changes in sun angle and haze level. Three of the algorithms were tested on a simulated data set, and all of the algorithms were tested on consecutive-day data. The classification performance on the data sets using the algorithms is presented, along with results of statistical tests on the accuracy and proportion estimates. The three algorithms tested on the simulated data produced significant improvements over the results obtained using untransformed signatures. For the consecutive-day data, the tested algorithms produced improvements in most but not all cases. The tests indicated also that no statistically significant differences were noted among the algorithms.

Abotteen, R.

Minimization versus homotopy algorithms

The relative merits and demerits of the minimization techniques are assessed using globally convergent quasi-Newton algorithms on the one hand and the homotopy algorithms on the other hand for the solution of problems of nonlinear structural analysis. Like the homotopy algorithms, the globally convergent quasi-Newton algorithms are equally suited for the solution of the nonlinear equations of structural analysis directly without having to pose the problem as an equivalent minimization problem. In the close neighborhood of the limit and bifurcation points quasi-Newton algorithms experience difficulties. Homotopy algorithms are robust for practically all types of nonlinear problems but are computationally not as cost effective since they provide an extremely accurate prediction of the response by calculating it as a large number of points. Globally convergent algorithms can perform well with very approximate Hessians, while homotopy algorithms require extremely accurate Hessians. While quasi-Newton algorithms can be very easily structured to exploit sparsity and symmetry, homotopy algorithms are not presently so structured and would require special modifications for exploitation of such features without sacrificing robustness and global convergence.

Kamat, M. P.

Digital signal processing algorithms for automatic voice recognition

The current digital signal analysis algorithms are investigated that are implemented in automatic voice recognition algorithms. Automatic voice recognition means, the capability of a computer to recognize and interact with verbal commands. The digital signal is focused on, rather than the linguistic, analysis of speech signal. Several digital signal processing algorithms are available for voice recognition. Some of these algorithms are: Linear Predictive Coding (LPC), Short-time Fourier Analysis, and Cepstrum Analysis. Among these algorithms, the LPC is the most widely used. This algorithm has short execution time and do not require large memory storage. However, it has several limitations due to the assumptions used to develop it. The other 2 algorithms are frequency domain algorithms with not many assumptions, but they are not widely implemented or investigated. However, with the recent advances in the digital technology, namely signal processors, these 2 frequency domain algorithms may be investigated in order to implement them in voice recognition. This research is concerned with real time, microprocessor based recognition algorithms.

Botros, Nazeih M.

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Nachtigal, Noel M.

A fast, uncoupled, compressible, two-dimensional, unsteady boundary layer algorithm with separation for engine inlets

A finite difference boundary layer algorithm was developed to model viscous effects when an inviscid core flow solution is given. This algorithm solved each boundary layer equation separately, then iterated to find a solution. Solving the boundary layer equations sequentially was 2.4 to 4.0 times faster than solving the boundary layer equations simultaneously. This algorithm used a modified Baldwin-Lomax turbulence model, a weighted average of forward and backward differencing of the pressure gradient, and a backward sweep of the pressure. With these modifications, the boundary layer algorithm was able to model flows with and without separation. The number of grid points used in the boundary layer algorithm affected the stability of the algorithm affected the stability of the algorithm as well as the accuracy of the predictions of friction coefficients and momentum thicknesses. Results of this boundary layer algorithm compared well with experimental observations of friction coefficients and momentum thicknesses. In addition, when used interactively with an inviscid flow algorithm, this boundary layer algorithm corrected for viscous effects to give a good match with experimental observations for pressures in a supersonic inlet.

Roach, Robert L.

Tests of a Semi-Analytical Case 1 and Gelbstoff Case 2 SeaWiFS Algorithm with a Global Data Set

A semi-analytical algorithm was tested with a total of 733 points of either unpackaged or packaged-pigment data, with corresponding algorithm parameters for each data type. The 'unpackaged' type consisted of data sets that were generally consistent with the Case 1 CZCS algorithm and other well calibrated data sets. The 'packaged' type consisted of data sets apparently containing somewhat more packaged pigments, requiring modification of the absorption parameters of the model consistent with the CalCOFI study area. This resulted in two equally divided data sets. A more thorough scrutiny of these and other data sets using a semianalytical model requires improved knowledge of the phytoplankton and gelbstoff of the specific environment studied. Since the semi-analytical algorithm is dependent upon 4 spectral channels including the 412 nm channel, while most other algorithms are not, a means of testing data sets for consistency was sought. A numerical filter was developed to classify data sets into the above classes. The filter uses reflectance ratios, which can be determined from space. The sensitivity of such numerical filters to measurement resulting from atmospheric correction and sensor noise errors requires further study. The semi-analytical algorithm performed superbly on each of the data sets after classification, resulting in RMS1 errors of 0.107 and 0.121, respectively, for the unpackaged and packaged data-set classes, with little bias and slopes near 1.0. In combination, the RMS1 performance was 0.114. While these numbers appear rather sterling, one must bear in mind what mis-classification does to the results. Using an average or compromise parameterization on the modified global data set yielded an RMS1 error of 0.171, while using the unpackaged parameterization on the global evaluation data set yielded an RMS1 error of 0.284. So, without classification, the algorithm performs better globally using the average parameters than it does using the unpackaged parameters. Finally, the effects of even more extreme pigment packaging must be examined in order to improve algorithm performance at high latitudes. Note, however, that the North Sea and Mississippi River plume studies contributed data to the packaged and unpackaged classess, respectively, with little effect on algorithm performance. This suggests that gelbstoff-rich Case 2 waters do not seriously degrade performance of the semi-analytical algorithm.

Carder, Kendall L.

Comparison of Radar Rainfall Retrieval Algorithms in Convective Rain During TOGA COARE

The authors compare deterministic and stochastic rain-rate retrieval algorithms by applying them to 14-GHz nadir-looking airborne radar reflectivity profiles acquired in tropical convective rain during the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment, The deterministic algorithms both use the path-integrated attenuation (PIA), measured by the surface reference technique, as a constraint. One deterministic algorithm corrects the k-R relation, while the second corrects the Z-R relation. The stochastic algorithms are based on applying an extended Kalman filter to the reflectivity profile. One employs radar reflectivity only; the other additionally uses the PIA. The authors find that the stochastic algorithm, which uses the PIA, is the most robust algorithm with regard to incorrect assumptions about the drop size distribution (DSD). The deterministic algorithm that uses the PIA to adjust the Z-R relation is also fairly robust and produces rain rates similar to the stochastic algorithm that uses the PIA, The deterministic algorithm that adjusts only the k-R relation and the stochastic radar-only algorithm are more sensitive to assumptions about the DSD. It is likely that they underestimate convective rainfall, especially if the DSD is erroneously assumed to be appropriate for stratiform rain conditions.

Durden, Stephen L.

Evaluation of Various Radar Data Quality Control Algorithms Based on Accumulated Radar Rainfall Statistics

The primary function of the TRMM Ground Validation (GV) Program is to create GV rainfall products that provide basic validation of satellite-derived precipitation measurements for select primary sites. A fundamental and extremely important step in creating high-quality GV products is radar data quality control. Quality control (QC) processing of TRMM GV radar data is based on some automated procedures, but the current QC algorithm is not fully operational and requires significant human interaction to assure satisfactory results. Moreover, the TRMM GV QC algorithm, even with continuous manual tuning, still can not completely remove all types of spurious echoes. In an attempt to improve the current operational radar data QC procedures of the TRMM GV effort, an intercomparison of several QC algorithms has been conducted. This presentation will demonstrate how various radar data QC algorithms affect accumulated radar rainfall products. In all, six different QC algorithms will be applied to two months of WSR-88D radar data from Melbourne, Florida. Daily, five-day, and monthly accumulated radar rainfall maps will be produced for each quality-controlled data set. The QC algorithms will be evaluated and compared based on their ability to remove spurious echoes without removing significant precipitation. Strengths and weaknesses of each algorithm will be assessed based on, their abilit to mitigate both erroneous additions and reductions in rainfall accumulation from spurious echo contamination and true precipitation removal, respectively. Contamination from individual spurious echo categories will be quantified to further diagnose the abilities of each radar QC algorithm. Finally, a cost-benefit analysis will be conducted to determine if a more automated QC algorithm is a viable alternative to the current, labor-intensive QC algorithm employed by TRMM GV.

Robinson, Michael

The Langley Parameterized Shortwave Algorithm (LPSA) for Surface Radiation Budget Studies

An efficient algorithm was developed during the late 1980's and early 1990's by W. F. Staylor at NASA/LaRC for the purpose of deriving shortwave surface radiation budget parameters on a global scale. While the algorithm produced results in good agreement with observations, the lack of proper documentation resulted in a weak acceptance by the science community. The primary purpose of this report is to develop detailed documentation of the algorithm. In the process, the algorithm was modified whenever discrepancies were found between the algorithm and its referenced literature sources. In some instances, assumptions made in the algorithm could not be justified and were replaced with those that were justifiable. The algorithm uses satellite and operational meteorological data for inputs. Most of the original data sources have been replaced by more recent, higher quality data sources, and fluxes are now computed on a higher spatial resolution. Many more changes to the basic radiation scheme and meteorological inputs have been proposed to improve the algorithm and make the product more useful for new research projects. Because of the many changes already in place and more planned for the future, the algorithm has been renamed the Langley Parameterized Shortwave Algorithm (LPSA).

Gupta, Shashi K.

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental building block in numerous image processing applications. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute the coordinates of a set of cluster centers in d-space, such that those centers minimize the mean squared distance from each data point to its nearest center. This clustering algorithm is similar to another well-known clustering method, called k-means. One significant feature of ISOCLUS over k-means is that the actual number of clusters reported might be fewer or more than the number supplied as part of the input. The algorithm uses different heuristics to determine whether to merge lor split clusters. As ISOCLUS can run very slowly, particularly on large data sets, there has been a growing .interest in the remote sensing community in computing it efficiently. We have developed a faster implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm of Kanungo, et al. They showed that, by using a kd-tree data structure for storing the data, it is possible to reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm, and we show that it is possible to achieve essentially the same results as ISOCLUS on large data sets, but with significantly lower running times. This adaptation involves computing a number of cluster statistics that are needed for ISOCLUS but not for k-means. Both the k-means and ISOCLUS algorithms are based on iterative schemes, in which nearest neighbors are calculated until some convergence criterion is satisfied. Each iteration requires that the nearest center for each data point be computed. Naively, this requires O(kn) time, where k denotes the current number of centers. Traditional techniques for accelerating nearest neighbor searching involve storing the k centers in a data structure. However, because of the iterative nature of the algorithm, this data structure would need to be rebuilt with each new iteration. Our approach is to store the data points in a kd-tree data structure. The assignment of points to nearest neighbors is carried out by a filtering process, which successively eliminates centers that can not possibly be the nearest neighbor for a given region of space. This algorithm is significantly faster, because large groups of data points can be assigned to their nearest center in a single operation. Preliminary results on a number of real Landsat datasets show that our revised ISOCLUS-like scheme runs about twice as fast.

Memarsadeghi, Nargess

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

Houck, Jacob A.

Motion Cueing Algorithm Development: Human-Centered Linear and Nonlinear Approaches

While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. Prior research identified viable features from two algorithms: the nonlinear "adaptive algorithm", and the "optimal algorithm" that incorporates human vestibular models. A novel approach to motion cueing, the "nonlinear algorithm" is introduced that combines features from both approaches. This algorithm is formulated by optimal control, and incorporates a new integrated perception model that includes both visual and vestibular sensation and the interaction between the stimuli. Using a time-varying control law, the matrix Riccati equation is updated in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. The neurocomputing approach was crucial in that the number of presentations of an input vector could be reduced to meet the real time requirement without degrading the quality of the motion cues.

Houck, Jacob A.

Design and Implementation of the Automated Rendezvous Targeting Algorithms for Orion

The Orion vehicle will be designed to perform several rendezvous missions: rendezvous with the ISS in Low Earth Orbit (LEO), rendezvous with the EDS/Altair in LEO, a contingency rendezvous with the ascent stage of the Altair in Low Lunar Orbit (LLO) and a contingency rendezvous in LLO with the ascent and descent stage in the case of an aborted lunar landing. Therefore, it is not difficult to realize that each of these scenarios imposes different operational, timing, and performance constraints on the GNC system. To this end, a suite of on-board guidance and targeting algorithms have been designed to meet the requirement to perform the rendezvous independent of communications with the ground. This capability is particularly relevant for the lunar missions, some of which may occur on the far side of the moon. This paper will describe these algorithms which are designed to be structured and arranged in such a way so as to be flexible and able to safely perform a wide variety of rendezvous trajectories. The goal of the algorithms is not to merely fly one specific type of canned rendezvous profile. Conversely, it was designed from the start to be general enough such that any type of trajectory profile can be flown.(i.e. a coelliptic profile, a stable orbit rendezvous profile, and a expedited LLO rendezvous profile, etc) all using the same rendezvous suite of algorithms. Each of these profiles makes use of maneuver types which have been designed with dual goals of robustness and performance. They are designed to converge quickly under dispersed conditions and they are designed to perform many of the functions performed on the ground today. The targeting algorithms consist of a phasing maneuver (NC), an altitude adjust maneuver (NH), and plane change maneuver (NPC), a coelliptic maneuver (NSR), a Lambert targeted maneuver, and several multiple-burn targeted maneuvers which combine one of more of these algorithms. The derivation and implementation of each of these algorithms will be discussed in detail, as well and the Rendezvous Targeting "wrapper" which will sequentially tie them all together into a single onboard targeting tool which can produce a final integrated rendezvous trajectory. In a similar fashion, the various guidance modes available for flying out each of these maneuvers will be discussed as well. This paradigm of having the onboard guidance & targeting capability described above is different than the way the Space Shuttle has operated thus far. As a result, a discussion of these differences in terms of operations and ground and crew intervention will also be discussed. However, the general framework of how the mission designers on the ground first perform all mission design and planning functions, and then uplink that burn plan to the vehicle ensures that the ground will be involved to ensure safety and reliability. The only real difference is which of these functions will be done onboard vs. on the ground as done currently. Finally, this paper will describe the performance of each of these algorithms individually as well as the entire suite of algorithms as applied to the Orion ISS and EDS/Altair rendezvous missions in LEO. These algorithms have been incorporated in both a Linear Covariance environment and a Monte Carlo environment and the results of these dispersion analyses will be presented in the paper as well.

DSouza, Christopher

Synthesis of Greedy Algorithms Using Dominance Relations

Greedy algorithms exploit problem structure and constraints to achieve linear-time performance. Yet there is still no completely satisfactory way of constructing greedy algorithms. For example, the Greedy Algorithm of Edmonds depends upon translating a problem into an algebraic structure called a matroid, but the existence of such a translation can be as hard to determine as the existence of a greedy algorithm itself. An alternative characterization of greedy algorithms is in terms of dominance relations, a well-known algorithmic technique used to prune search spaces. We demonstrate a process by which dominance relations can be methodically derived for a number of greedy algorithms, including activity selection, and prefix-free codes. By incorporating our approach into an existing framework for algorithm synthesis, we demonstrate that it could be the basis for an effective engineering method for greedy algorithms. We also compare our approach with other characterizations of greedy algorithms.

Nedunuri, Srinivas

Recent Advancements in Lightning Jump Algorithm Work

In the past year, the primary objectives were to show the usefulness of total lightning as compared to traditional cloud-to-ground (CG) networks, test the lightning jump algorithm configurations in other regions of the country, increase the number of thunderstorms within our thunderstorm database, and to pinpoint environments that could prove difficult for any lightning jump configuration. A total of 561 thunderstorms have been examined in the past year (409 non-severe, 152 severe) from four regions of the country (North Alabama, Washington D.C., High Plains of CO/KS, and Oklahoma). Results continue to indicate that the 2 lightning jump algorithm configuration holds the most promise in terms of prospective operational lightning jump algorithms, with a probability of detection (POD) at 81%, a false alarm rate (FAR) of 45%, a critical success index (CSI) of 49% and a Heidke Skill Score (HSS) of 0.66. The second best performing algorithm configuration was the Threshold 4 algorithm, which had a POD of 72%, FAR of 51%, a CSI of 41% and an HSS of 0.58. Because a more complex algorithm configuration shows the most promise in terms of prospective operational lightning jump algorithms, accurate thunderstorm cell tracking work must be undertaken to track lightning trends on an individual thunderstorm basis over time. While these numbers for the 2 configuration are impressive, the algorithm does have its weaknesses. Specifically, low-topped and tropical cyclone thunderstorm environments are present issues for the 2 lightning jump algorithm, because of the suppressed vertical depth impact on overall flash counts (i.e., a relative dearth in lightning). For example, in a sample of 120 thunderstorms from northern Alabama that contained 72 missed events by the 2 algorithm 36% of the misses were associated with these two environments (17 storms).

Schultz, Christopher J.

Conservative Patch Algorithm and Mesh Sequencing for PAB3D

A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.

Pao, S. P.